1.6.0-DEV-3bfcb743c2.log

Julia Version 1.6.0-DEV.1185
Commit 3bfcb743c2 (2020-10-11 23:29 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: AMD EPYC 7502 32-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-10.0.1 (ORCJIT, znver2)
Environment:
  JULIA_DEPOT_PATH = ::/usr/local/share/julia
  JULIA_NUM_THREADS = 2
  JULIA_MAX_NUM_PRECOMPILE_FILES = 9223372036854775807

  Resolving package versions...
  Installed IniFile ───────────── v0.5.0
  Installed MbedTLS_jll ───────── v2.16.8+0
  Installed BenchmarkTools ────── v0.4.3
  Installed MbedTLS ───────────── v1.0.2
  Installed HTTP ──────────────── v0.8.19
  Installed AbstractAlgebra ───── v0.8.1
  Installed DocStringExtensions ─ v0.8.3
  Installed JSON ──────────────── v0.21.1
  Installed Parsers ───────────── v1.0.11
  Installed BinaryProvider ────── v0.5.10
  Installed Nemo ──────────────── v0.16.4
  Installed IntegerTriangles ──── v0.1.0
Updating `~/.julia/environments/v1.6/Project.toml`
  [715aea54] + IntegerTriangles v0.1.0
Updating `~/.julia/environments/v1.6/Manifest.toml`
  [c3fe647b] + AbstractAlgebra v0.8.1
  [6e4b80f9] + BenchmarkTools v0.4.3
  [b99e7846] + BinaryProvider v0.5.10
  [ffbed154] + DocStringExtensions v0.8.3
  [cd3eb016] + HTTP v0.8.19
  [83e8ac13] + IniFile v0.5.0
  [715aea54] + IntegerTriangles v0.1.0
  [682c06a0] + JSON v0.21.1
  [739be429] + MbedTLS v1.0.2
  [c8ffd9c3] + MbedTLS_jll v2.16.8+0
  [2edaba10] + Nemo v0.16.4
  [69de0a69] + Parsers v1.0.11
  [56f22d72] + Artifacts
  [2a0f44e3] + Base64
  [ade2ca70] + Dates
  [b77e0a4c] + InteractiveUtils
  [76f85450] + LibGit2
  [8f399da3] + Libdl
  [37e2e46d] + LinearAlgebra
  [56ddb016] + Logging
  [d6f4376e] + Markdown
  [a63ad114] + Mmap
  [44cfe95a] + Pkg
  [de0858da] + Printf
  [3fa0cd96] + REPL
  [9a3f8284] + Random
  [ea8e919c] + SHA
  [9e88b42a] + Serialization
  [6462fe0b] + Sockets
  [2f01184e] + SparseArrays
  [10745b16] + Statistics
  [fa267f1f] + TOML
  [8dfed614] + Test
  [cf7118a7] + UUIDs
  [4ec0a83e] + Unicode
   Building Nemo → `~/.julia/scratchspaces/44cfe95a-1eb2-52ea-b672-e2afdf69b78f/43329acc110bd582d83d9cc4e4f5a902d2bcb262/build.log`
    Testing IntegerTriangles
Status `/tmp/jl_5umq4W/Project.toml`
  [c3fe647b] AbstractAlgebra v0.8.1
  [6e4b80f9] BenchmarkTools v0.4.3
  [ffbed154] DocStringExtensions v0.8.3
  [cd3eb016] HTTP v0.8.19
  [715aea54] IntegerTriangles v0.1.0
  [2edaba10] Nemo v0.16.4
  [8dfed614] Test
Status `/tmp/jl_5umq4W/Manifest.toml`
  [c3fe647b] AbstractAlgebra v0.8.1
  [6e4b80f9] BenchmarkTools v0.4.3
  [b99e7846] BinaryProvider v0.5.10
  [ffbed154] DocStringExtensions v0.8.3
  [cd3eb016] HTTP v0.8.19
  [83e8ac13] IniFile v0.5.0
  [715aea54] IntegerTriangles v0.1.0
  [682c06a0] JSON v0.21.1
  [739be429] MbedTLS v1.0.2
  [c8ffd9c3] MbedTLS_jll v2.16.8+0
  [2edaba10] Nemo v0.16.4
  [69de0a69] Parsers v1.0.11
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [b77e0a4c] InteractiveUtils
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [44cfe95a] Pkg
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA
  [9e88b42a] Serialization
  [6462fe0b] Sockets
  [2f01184e] SparseArrays
  [10745b16] Statistics
  [fa267f1f] TOML
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
    Testing Running tests...
A000001 -> b05aac3a
A000002 -> a16fdce1
A000003 -> dce59dfa
A000004 -> e08c91ee
A000005 -> dc68ce2d
A000006 -> cc1c5eef
A000007 -> a0fb5fa7
A000008 -> 6b89869c
A000009 -> 7b1a68fd
A000010 -> 8f2cabce
A000011 -> 0fbe94c2
A000012 -> be47c5ad
A000013 -> ce5df89a
A000014 -> cdcf8fe9
A000015 -> ef1dfb27
A000016 -> faef93b4
A000017 -> 9a18469a
A000018 -> acf8e19d
A000019 -> f7bd4523
A000020 -> fb21755a
A000021 -> 9dcc9ff5
A000022 -> 96373cad
A000023 -> 90ff9f2c
A000024 -> 732cce4b
A000025 -> e5d8b8b9
A000026 -> 97b68cc8
A000027 -> ef6e981b
A000028 -> d9e78112
A000029 -> 8eecebee
A000030 -> 6fc9ada8
A000031 -> 8a73fb8a
A000032 -> fc87efaf
A000033 -> ded80b59
A000034 -> efaf637b
A000035 -> be47c5ad
A000036 -> e9abff85
A000037 -> 8a1b4cfa
A000038 -> 60f8dc48
A000039 -> 23a89c49
A000040 -> 70fa3a7d
A000041 -> c990eede
A000042 -> a1825853
A000043 -> 8a791959
A000044 -> ea937207
A000045 -> 8a9ca1ad
A000046 -> 295d4eb9
A000047 -> f69de8a9
A000048 -> 0e89b5fe
A000049 -> af89ddd4
A000050 -> 16c55b4b
A000051 -> dafabe94
A000052 -> cf6f40e9
A000053 -> 9eaf8cc4
A000054 -> ebe0605e
A000055 -> 6bfeefb7
A000056 -> ec83c1a1
A000057 -> 34a529ef
A000058 -> bc4fb6cf
A000059 -> 9c8ff8a8
A000060 -> 5b8eea60
A000061 -> ecd66217
A000062 -> afb620d0
A000063 -> 742d8af3
A000064 -> 647dcdce
A000065 -> ab3f29bc
A000066 -> a482c74a
A000067 -> bdfcb86f
A000068 -> a8dd91dd
A000069 -> e8012b0f
A000070 -> bbcde8ca
A000071 -> 50fe5b5c
A000072 -> e09e9a3f
A000073 -> efdac6ee
A000074 -> cb88be99
A000075 -> af48da1a
A000076 -> fb391ca3
A000077 -> dfff1eb0
A000078 -> 2ed8ecef
A000079 -> de55f23c
A000080 -> ea71d69c
A000081 -> c6368183
A000082 -> 7cceffef
A000083 -> a74d9387
A000084 -> fef6d0d8
A000085 -> 021dbce9
A000086 -> a7e8bddf
A000087 -> aaa11155
A000088 -> d1bf4ce8
A000089 -> 8ecefa7c
A000090 -> 761ef802
A000091 -> fdf8d8ee
A000092 -> 7fa71ff3
A000093 -> aa5df9fb
A000094 -> 05cd83b6
A000095 -> 75b2bb5a
A000096 -> 7cd77e84
A000097 -> ba228f94
A000098 -> 57fe4493
A000099 -> 530b8842
A000100 -> 586e57f3
 A000029
Searching for: c85ebeb0
Matches: 0
 A000085 A212915 A212916 A229053 A229068 A239080 A239081 A239082

f9e5dcb7
No match!

bdfdff8d
No match!
Test Summary: | Pass  Total
Laguerre      |   13     13

=================
BinomialTriangle 

Triangle:  [1, 1, 1, 1, 2, 1, 1, 3]
Sum:       [1, 2, 4, 8, 16, 32, 64, 128]
EvenSum:   [1, 1, 2, 4, 8, 16, 32, 64]
OddSum:    [0, 1, 2, 4, 8, 16, 32, 64]
AltSum:    [1, 0, 0, 0, 0, 0, 0, 0]
DiagSum:   [1, 1, 2, 3, 5, 8, 13, 21]
Central:   [1, 2, 6, 20]
LeftSide:  [1, 1, 1, 1, 1, 1, 1, 1]
RightSide: [1, 1, 1, 1, 1, 1, 1, 1]
PosHalf:   [1, 3, 9, 27, 81, 243, 729, 2187]
NegHalf:   [1, -1, 1, -1, 1, -1, 1, -1]
N0TS:      [0, 1, 4, 12, 32, 80, 192, 448]
NATS:      [1, 3, 8, 20, 48, 112, 256, 576]


Triangle:

[1]
[1, 1]
[1, 2, 1]
[1, 3, 3, 1]
[1, 4, 6, 4, 1]
[1, 5, 10, 10, 5, 1]
[1, 6, 15, 20, 15, 6, 1]
[1, 7, 21, 35, 35, 21, 7, 1]

Flat triangle:  [1, 1, 1, 1, 2, 1, 1, 3]

Inverse triangle:

[1]
[-1, 1]
[1, -2, 1]
[-1, 3, -3, 1]
[1, -4, 6, -4, 1]
[-1, 5, -10, 10, -5, 1]
[1, -6, 15, -20, 15, -6, 1]
[-1, 7, -21, 35, -35, 21, -7, 1]

Inverse:  [1, -1, 1, 1, -2, 1, -1, 3]

Diagonal triangle:

[1]
[1]
[1, 1]
[1, 2]
[1, 3, 1]
[1, 4, 3]
[1, 5, 6, 1]
[1, 6, 10, 4]

Diagonal:  [1, 1, 1, 1, 1, 2, 1, 3]

Polynomial values, array:

[1, 1, 1, 1, 1, 1, 1, 1]
[1, 2, 3, 4, 5, 6, 7, 8]
[1, 4, 9, 16, 25, 36, 49, 64]
[1, 8, 27, 64, 125, 216, 343, 512]
[1, 16, 81, 256, 625, 1296, 2401, 4096]
[1, 32, 243, 1024, 3125, 7776, 16807, 32768]
[1, 64, 729, 4096, 15625, 46656, 117649, 262144]
[1, 128, 2187, 16384, 78125, 279936, 823543, 2097152]

Polynomial values, triangle:

[1]
[1, 1]
[1, 2, 1]
[1, 4, 3, 1]
[1, 8, 9, 4, 1]
[1, 16, 27, 16, 5, 1]
[1, 32, 81, 64, 25, 6, 1]
[1, 64, 243, 256, 125, 36, 7, 1]

PolyVal:  [1, 1, 1, 1, 2, 1, 1, 4]


=================
LaguerreTriangle 

Triangle:  [1, 1, 1, 2, 4, 1, 6, 18]
Sum:       [1, 2, 7, 34, 209, 1546, 13327, 130922]
EvenSum:   [1, 1, 3, 15, 97, 745, 6571, 65359]
OddSum:    [0, 1, 4, 19, 112, 801, 6756, 65563]
AltSum:    [1, 0, -1, -4, -15, -56, -185, -204]
DiagSum:   [1, 1, 3, 10, 43, 225, 1393, 9976]
Central:   [1, 4, 72, 2400]
LeftSide:  [1, 1, 2, 6, 24, 120, 720, 5040]
RightSide: [1, 1, 1, 1, 1, 1, 1, 1]
PosHalf:   [1, 3, 17, 139, 1473, 19091, 291793, 5129307]
NegHalf:   [1, -1, 1, 7, -127, 1711, -23231, 334391]
N0TS:      [0, 1, 6, 39, 292, 2505, 24306, 263431]
NATS:      [1, 3, 13, 73, 501, 4051, 37633, 394353]


Triangle:

[1]
[1, 1]
[2, 4, 1]
[6, 18, 9, 1]
[24, 96, 72, 16, 1]
[120, 600, 600, 200, 25, 1]
[720, 4320, 5400, 2400, 450, 36, 1]
[5040, 35280, 52920, 29400, 7350, 882, 49, 1]

Flat triangle:  [1, 1, 1, 2, 4, 1, 6, 18]

Inverse triangle:

[1]
[-1, 1]
[2, -4, 1]
[-6, 18, -9, 1]
[24, -96, 72, -16, 1]
[-120, 600, -600, 200, -25, 1]
[720, -4320, 5400, -2400, 450, -36, 1]
[-5040, 35280, -52920, 29400, -7350, 882, -49, 1]

Inverse:  [1, -1, 1, 2, -4, 1, -6, 18]

Diagonal triangle:

[1]
[1]
[2, 1]
[6, 4]
[24, 18, 1]
[120, 96, 9]
[720, 600, 72, 1]
[5040, 4320, 600, 16]

Diagonal:  [1, 1, 2, 1, 6, 4, 24, 18]

Polynomial values, array:

[1, 1, 1, 1, 1, 1, 1, 1]
[1, 2, 3, 4, 5, 6, 7, 8]
[2, 7, 14, 23, 34, 47, 62, 79]
[6, 34, 86, 168, 286, 446, 654, 916]
[24, 209, 648, 1473, 2840, 4929, 7944, 12113]
[120, 1546, 5752, 14988, 32344, 61870, 108696, 179152]
[720, 13327, 58576, 173007, 414160, 866695, 1649232, 2921911]
[5040, 130922, 671568, 2228544, 5876336, 13373190, 27422352, 51988748]

Polynomial values, triangle:

[1]
[1, 1]
[2, 2, 1]
[6, 7, 3, 1]
[24, 34, 14, 4, 1]
[120, 209, 86, 23, 5, 1]
[720, 1546, 648, 168, 34, 6, 1]
[5040, 13327, 5752, 1473, 286, 47, 7, 1]

PolyVal:  [1, 1, 1, 2, 2, 1, 6, 7]


=================
LahTriangle 

Triangle:  [1, 0, 1, 0, 2, 1, 0, 6]
Sum:       [1, 1, 3, 13, 73, 501, 4051, 37633]
EvenSum:   [1, 0, 1, 6, 37, 260, 2101, 19362]
OddSum:    [0, 1, 2, 7, 36, 241, 1950, 18271]
AltSum:    [1, -1, -1, -1, 1, 19, 151, 1091]
DiagSum:   [1, 0, 1, 2, 7, 30, 157, 972]
Central:   [1, 2, 36, 1200]
LeftSide:  [1, 0, 0, 0, 0, 0, 0, 0]
RightSide: [1, 1, 1, 1, 1, 1, 1, 1]
PosHalf:   [1, 1, 5, 37, 361, 4361, 62701, 1044205]
NegHalf:   [1, 1, -3, 13, -71, 441, -2699, 9157]
N0TS:      [0, 1, 4, 21, 136, 1045, 9276, 93289]
NATS:      [1, 2, 7, 34, 209, 1546, 13327, 130922]


Triangle:

[1]
[0, 1]
[0, 2, 1]
[0, 6, 6, 1]
[0, 24, 36, 12, 1]
[0, 120, 240, 120, 20, 1]
[0, 720, 1800, 1200, 300, 30, 1]
[0, 5040, 15120, 12600, 4200, 630, 42, 1]

Flat triangle:  [1, 0, 1, 0, 2, 1, 0, 6]

Inverse triangle:

[1]
[0, 1]
[0, -2, 1]
[0, 6, -6, 1]
[0, -24, 36, -12, 1]
[0, 120, -240, 120, -20, 1]
[0, -720, 1800, -1200, 300, -30, 1]
[0, 5040, -15120, 12600, -4200, 630, -42, 1]

Inverse:  [1, 0, 1, 0, -2, 1, 0, 6]

Diagonal triangle:

[1]
[0]
[0, 1]
[0, 2]
[0, 6, 1]
[0, 24, 6]
[0, 120, 36, 1]
[0, 720, 240, 12]

Diagonal:  [1, 0, 0, 1, 0, 2, 0, 6]

Polynomial values, array:

[1, 1, 1, 1, 1, 1, 1, 1]
[0, 1, 2, 3, 4, 5, 6, 7]
[0, 3, 8, 15, 24, 35, 48, 63]
[0, 13, 44, 99, 184, 305, 468, 679]
[0, 73, 304, 801, 1696, 3145, 5328, 8449]
[0, 501, 2512, 7623, 18144, 37225, 68976, 118587]
[0, 4051, 24064, 83079, 220096, 495475, 997056, 1846999]
[0, 37633, 261536, 1017495, 2977216, 7306325, 15877728, 31535371]

Polynomial values, triangle:

[1]
[0, 1]
[0, 1, 1]
[0, 3, 2, 1]
[0, 13, 8, 3, 1]
[0, 73, 44, 15, 4, 1]
[0, 501, 304, 99, 24, 5, 1]
[0, 4051, 2512, 801, 184, 35, 6, 1]

PolyVal:  [1, 0, 1, 0, 1, 1, 0, 3]


=================
CatalanTriangle 

Triangle:  [1, 0, 1, 1, 0, 1, 0, 2]
Sum:       [1, 1, 2, 3, 6, 10, 20, 35]
EvenSum:   [1, 0, 2, 0, 6, 0, 20, 0]
OddSum:    [0, 1, 0, 3, 0, 10, 0, 35]
AltSum:    [1, -1, 2, -3, 6, -10, 20, -35]
DiagSum:   [1, 0, 2, 0, 5, 0, 14, 0]
Central:   [1, 0, 3, 0]
LeftSide:  [1, 0, 1, 0, 2, 0, 5, 0]
RightSide: [1, 1, 1, 1, 1, 1, 1, 1]
PosHalf:   [1, 1, 5, 9, 45, 97, 485, 1145]
NegHalf:   [1, 1, 5, 9, 45, 97, 485, 1145]
N0TS:      [0, 1, 2, 5, 10, 22, 44, 93]
NATS:      [1, 2, 4, 8, 16, 32, 64, 128]


Triangle:

[1]
[0, 1]
[1, 0, 1]
[0, 2, 0, 1]
[2, 0, 3, 0, 1]
[0, 5, 0, 4, 0, 1]
[5, 0, 9, 0, 5, 0, 1]
[0, 14, 0, 14, 0, 6, 0, 1]

Flat triangle:  [1, 0, 1, 1, 0, 1, 0, 2]

Inverse triangle:

[1]
[0, 1]
[-1, 0, 1]
[0, -2, 0, 1]
[1, 0, -3, 0, 1]
[0, 3, 0, -4, 0, 1]
[-1, 0, 6, 0, -5, 0, 1]
[0, -4, 0, 10, 0, -6, 0, 1]

Inverse:  [1, 0, 1, -1, 0, 1, 0, -2]

Diagonal triangle:

[1]
[0]
[1, 1]
[0, 0]
[2, 2, 1]
[0, 0, 0]
[5, 5, 3, 1]
[0, 0, 0, 0]

Diagonal:  [1, 0, 1, 1, 0, 0, 2, 2]

Polynomial values, array:

[1, 1, 1, 1, 1, 1, 1, 1]
[0, 1, 2, 3, 4, 5, 6, 7]
[1, 2, 5, 10, 17, 26, 37, 50]
[0, 3, 12, 33, 72, 135, 228, 357]
[2, 6, 30, 110, 306, 702, 1406, 2550]
[0, 10, 74, 366, 1300, 3650, 8670, 18214]
[5, 20, 185, 1220, 5525, 18980, 53465, 130100]
[0, 35, 460, 4065, 23480, 98695, 329700, 929285]

Polynomial values, triangle:

[1]
[0, 1]
[1, 1, 1]
[0, 2, 2, 1]
[2, 3, 5, 3, 1]
[0, 6, 12, 10, 4, 1]
[5, 10, 30, 33, 17, 5, 1]
[0, 20, 74, 110, 72, 26, 6, 1]

PolyVal:  [1, 0, 1, 1, 1, 1, 0, 2]


=================
MotzkinTriangle 

Triangle:  [1, 1, 1, 2, 2, 1, 4, 5]
Sum:       [1, 2, 5, 13, 35, 96, 267, 750]
EvenSum:   [1, 1, 3, 7, 19, 51, 141, 393]
OddSum:    [0, 1, 2, 6, 16, 45, 126, 357]
AltSum:    [1, 0, 1, 1, 3, 6, 15, 36]
DiagSum:   [1, 1, 3, 6, 15, 36, 91, 232]
Central:   [1, 2, 9, 44]
LeftSide:  [1, 1, 2, 4, 9, 21, 51, 127]
RightSide: [1, 1, 1, 1, 1, 1, 1, 1]
PosHalf:   [1, 3, 13, 59, 285, 1419, 7245, 37659]
NegHalf:   [1, -1, 5, -17, 77, -345, 1653, -8097]
N0TS:      [0, 1, 4, 14, 46, 147, 462, 1437]
NATS:      [1, 3, 9, 27, 81, 243, 729, 2187]


Triangle:

[1]
[1, 1]
[2, 2, 1]
[4, 5, 3, 1]
[9, 12, 9, 4, 1]
[21, 30, 25, 14, 5, 1]
[51, 76, 69, 44, 20, 6, 1]
[127, 196, 189, 133, 70, 27, 7, 1]

Flat triangle:  [1, 1, 1, 2, 2, 1, 4, 5]

Inverse triangle:

[1]
[-1, 1]
[0, -2, 1]
[1, 1, -3, 1]
[-1, 2, 3, -4, 1]
[0, -4, 2, 6, -5, 1]
[1, 2, -9, 0, 10, -6, 1]
[-1, 3, 9, -15, -5, 15, -7, 1]

Inverse:  [1, -1, 1, 0, -2, 1, 1, 1]

Diagonal triangle:

[1]
[1]
[2, 1]
[4, 2]
[9, 5, 1]
[21, 12, 3]
[51, 30, 9, 1]
[127, 76, 25, 4]

Diagonal:  [1, 1, 2, 1, 4, 2, 9, 5]

Polynomial values, array:

[1, 1, 1, 1, 1, 1, 1, 1]
[1, 2, 3, 4, 5, 6, 7, 8]
[2, 5, 10, 17, 26, 37, 50, 65]
[4, 13, 34, 73, 136, 229, 358, 529]
[9, 35, 117, 315, 713, 1419, 2565, 4307]
[21, 96, 405, 1362, 3741, 8796, 18381, 35070]
[51, 267, 1407, 5895, 19635, 54531, 131727, 285567]
[127, 750, 4899, 25528, 103071, 338082, 944035, 2325324]

Polynomial values, triangle:

[1]
[1, 1]
[2, 2, 1]
[4, 5, 3, 1]
[9, 13, 10, 4, 1]
[21, 35, 34, 17, 5, 1]
[51, 96, 117, 73, 26, 6, 1]
[127, 267, 405, 315, 136, 37, 7, 1]

PolyVal:  [1, 1, 1, 2, 2, 1, 4, 5]


=================
NarayanaTriangle 

Triangle:  [1, 0, 1, 0, 1, 1, 0, 1]
Sum:       [1, 1, 2, 5, 14, 42, 132, 429]
EvenSum:   [1, 0, 1, 3, 7, 20, 66, 217]
OddSum:    [0, 1, 1, 2, 7, 22, 66, 212]
AltSum:    [1, -1, 0, 1, 0, -2, 0, 5]
DiagSum:   [1, 0, 1, 1, 2, 4, 8, 17]
Central:   [1, 1, 6, 50, 490]
LeftSide:  [1, 0, 0, 0, 0, 0, 0, 0]
RightSide: [1, 1, 1, 1, 1, 1, 1, 1]
PosHalf:   [1, 1, 3, 11, 45, 197, 903, 4279]
NegHalf:   [1, 1, -1, -1, 5, -3, -21, 51]
N0TS:      [0, 1, 3, 10, 35, 126, 462, 1716]
NATS:      [1, 2, 5, 15, 49, 168, 594, 2145]


Triangle:

[1]
[0, 1]
[0, 1, 1]
[0, 1, 3, 1]
[0, 1, 6, 6, 1]
[0, 1, 10, 20, 10, 1]
[0, 1, 15, 50, 50, 15, 1]
[0, 1, 21, 105, 175, 105, 21, 1]

Flat triangle:  [1, 0, 1, 0, 1, 1, 0, 1]

Inverse triangle:

[1]
[0, 1]
[0, -1, 1]
[0, 2, -3, 1]
[0, -7, 12, -6, 1]
[0, 39, -70, 40, -10, 1]
[0, -321, 585, -350, 100, -15, 1]
[0, 3681, -6741, 4095, -1225, 210, -21, 1]

Inverse:  [1, 0, 1, 0, -1, 1, 0, 2]

Diagonal triangle:

[1]
[0]
[0, 1]
[0, 1]
[0, 1, 1]
[0, 1, 3]
[0, 1, 6, 1]
[0, 1, 10, 6]

Diagonal:  [1, 0, 0, 1, 0, 1, 0, 1]

Polynomial values, array:

[1, 1, 1, 1, 1, 1, 1, 1, 1]
[0, 1, 2, 3, 4, 5, 6, 7, 8]
[0, 2, 6, 12, 20, 30, 42, 56, 72]
[0, 5, 22, 57, 116, 205, 330, 497, 712]
[0, 14, 90, 300, 740, 1530, 2814, 4760, 7560]
[0, 42, 394, 1686, 5028, 12130, 25422, 48174, 84616]
[0, 132, 1806, 9912, 35700, 100380, 239442, 507696, 985032]
[0, 429, 8558, 60213, 261780, 857405, 2326434, 5516133, 11814728]
[0, 1430, 41586, 374988, 1967300, 7503330, 23151030, 61363736, 145043208]

Polynomial values, triangle:

[1]
[0, 1]
[0, 1, 1]
[0, 2, 2, 1]
[0, 5, 6, 3, 1]
[0, 14, 22, 12, 4, 1]
[0, 42, 90, 57, 20, 5, 1]
[0, 132, 394, 300, 116, 30, 6, 1]

PolyVal:  [1, 0, 1, 0, 1, 1, 0, 2]


=================
SchroederBigTriangle 

Triangle:  [1, 2, 1, 6, 4, 1, 22, 16]
Sum:       [1, 3, 11, 45, 197, 903, 4279, 20793]
EvenSum:   [1, 2, 7, 28, 121, 550, 2591, 12536]
OddSum:    [0, 1, 4, 17, 76, 353, 1688, 8257]
AltSum:    [1, 1, 3, 11, 45, 197, 903, 4279]
DiagSum:   [1, 2, 7, 26, 107, 468, 2141, 10124]
Central:   [1, 4, 30, 264]
LeftSide:  [1, 2, 6, 22, 90, 394, 1806, 8558]
RightSide: [1, 1, 1, 1, 1, 1, 1, 1]
PosHalf:   [1, 5, 33, 253, 2121, 18853, 174609, 1667021]
NegHalf:   [1, -3, 17, -123, 1001, -8739, 79969, -756939]
N0TS:      [0, 1, 6, 31, 156, 785, 3978, 20335]
NATS:      [1, 4, 17, 76, 353, 1688, 8257, 41128]


Triangle:

[1]
[2, 1]
[6, 4, 1]
[22, 16, 6, 1]
[90, 68, 30, 8, 1]
[394, 304, 146, 48, 10, 1]
[1806, 1412, 714, 264, 70, 12, 1]
[8558, 6752, 3534, 1408, 430, 96, 14, 1]

Flat triangle:  [1, 2, 1, 6, 4, 1, 22, 16]

Inverse triangle:

[1]
[-2, 1]
[2, -4, 1]
[-2, 8, -6, 1]
[2, -12, 18, -8, 1]
[-2, 16, -38, 32, -10, 1]
[2, -20, 66, -88, 50, -12, 1]
[-2, 24, -102, 192, -170, 72, -14, 1]

Inverse:  [1, -2, 1, 2, -4, 1, -2, 8]

Diagonal triangle:

[1]
[2]
[6, 1]
[22, 4]
[90, 16, 1]
[394, 68, 6]
[1806, 304, 30, 1]
[8558, 1412, 146, 8]

Diagonal:  [1, 2, 6, 1, 22, 4, 90, 16]

Polynomial values, array:

[1, 1, 1, 1, 1, 1, 1, 1]
[2, 3, 4, 5, 6, 7, 8, 9]
[6, 11, 18, 27, 38, 51, 66, 83]
[22, 45, 86, 151, 246, 377, 550, 771]
[90, 197, 426, 861, 1610, 2805, 4602, 7181]
[394, 903, 2162, 4969, 10602, 20939, 38578, 66957]
[1806, 4279, 11166, 28911, 70078, 156591, 323694, 624631]
[8558, 20793, 58438, 169187, 464334, 1172293, 2717318, 5828463]

Polynomial values, triangle:

[1]
[2, 1]
[6, 3, 1]
[22, 11, 4, 1]
[90, 45, 18, 5, 1]
[394, 197, 86, 27, 6, 1]
[1806, 903, 426, 151, 38, 7, 1]
[8558, 4279, 2162, 861, 246, 51, 8, 1]

PolyVal:  [1, 2, 1, 6, 3, 1, 22, 11]


=================
JacobsthalTriangle 

Triangle:  [1, 1, 1, 1, 2, 1, 3, 5]
Sum:       [1, 2, 4, 12, 32, 88, 240, 656]
EvenSum:   [1, 1, 2, 6, 16, 44, 120, 328]
OddSum:    [0, 1, 2, 6, 16, 44, 120, 328]
AltSum:    [1, 0, 0, 0, 0, 0, 0, 0]
DiagSum:   [1, 1, 2, 5, 11, 26, 59, 137]
Central:   [1, 2, 10, 52]
LeftSide:  [1, 1, 1, 3, 5, 11, 21, 43]
RightSide: [1, 1, 1, 1, 1, 1, 1, 1]
PosHalf:   [1, 3, 9, 51, 225, 1083, 5049, 23811]
NegHalf:   [1, -1, 1, -9, 17, -89, 225, -937]
N0TS:      [0, 1, 4, 14, 48, 156, 496, 1544]
NATS:      [1, 3, 8, 26, 80, 244, 736, 2200]


Triangle:

[1]
[1, 1]
[1, 2, 1]
[3, 5, 3, 1]
[5, 12, 10, 4, 1]
[11, 27, 28, 16, 5, 1]
[21, 62, 75, 52, 23, 6, 1]
[43, 137, 193, 159, 85, 31, 7, 1]

Flat triangle:  [1, 1, 1, 1, 2, 1, 3, 5]

Inverse triangle:

[1]
[-1, 1]
[1, -2, 1]
[-1, 1, -3, 1]
[1, 4, 2, -4, 1]
[-1, -7, 10, 4, -5, 1]
[1, -14, -25, 16, 7, -6, 1]
[-1, 65, -21, -55, 21, 11, -7, 1]

Inverse:  [1, -1, 1, 1, -2, 1, -1, 1]

Diagonal triangle:

[1]
[1]
[1, 1]
[3, 2]
[5, 5, 1]
[11, 12, 3]
[21, 27, 10, 1]
[43, 62, 28, 4]

Diagonal:  [1, 1, 1, 1, 3, 2, 5, 5]

Polynomial values, array:

[1, 1, 1, 1, 1, 1, 1, 1]
[1, 2, 3, 4, 5, 6, 7, 8]
[1, 4, 9, 16, 25, 36, 49, 64]
[3, 12, 33, 72, 135, 228, 357, 528]
[5, 32, 117, 320, 725, 1440, 2597, 4352]
[11, 88, 417, 1424, 3895, 9096, 18893, 35872]
[21, 240, 1485, 6336, 20925, 57456, 137445, 295680]
[43, 656, 5289, 28192, 112415, 362928, 999901, 2437184]

Polynomial values, triangle:

[1]
[1, 1]
[1, 2, 1]
[3, 4, 3, 1]
[5, 12, 9, 4, 1]
[11, 32, 33, 16, 5, 1]
[21, 88, 117, 72, 25, 6, 1]
[43, 240, 417, 320, 135, 36, 7, 1]

PolyVal:  [1, 1, 1, 1, 2, 1, 3, 4]


=================
FibonacciTriangle 

Triangle:  [1, 1, 1, 1, 2, 1, 2, 4]
Sum:       [1, 2, 4, 10, 24, 58, 140, 338]
EvenSum:   [1, 1, 2, 5, 12, 29, 70, 169]
OddSum:    [0, 1, 2, 5, 12, 29, 70, 169]
AltSum:    [1, 0, 0, 0, 0, 0, 0, 0]
DiagSum:   [1, 1, 2, 4, 8, 16, 32, 64]
Central:   [1, 2, 8, 36]
LeftSide:  [1, 1, 1, 2, 3, 5, 8, 13]
RightSide: [1, 1, 1, 1, 1, 1, 1, 1]
PosHalf:   [1, 3, 9, 39, 153, 615, 2457, 9831]
NegHalf:   [1, -1, 1, -5, 9, -29, 65, -181]
N0TS:      [0, 1, 4, 13, 40, 117, 332, 921]
NATS:      [1, 3, 8, 23, 64, 175, 472, 1259]


Triangle:

[1]
[1, 1]
[1, 2, 1]
[2, 4, 3, 1]
[3, 8, 8, 4, 1]
[5, 15, 19, 13, 5, 1]
[8, 28, 42, 36, 19, 6, 1]
[13, 51, 89, 91, 60, 26, 7, 1]

Flat triangle:  [1, 1, 1, 1, 2, 1, 2, 4]

Inverse triangle:

[1]
[-1, 1]
[1, -2, 1]
[-1, 2, -3, 1]
[1, 0, 4, -4, 1]
[-1, -3, 0, 7, -5, 1]
[1, 2, -10, -2, 11, -6, 1]
[-1, 9, 14, -19, -7, 16, -7, 1]

Inverse:  [1, -1, 1, 1, -2, 1, -1, 2]

Diagonal triangle:

[1]
[1]
[1, 1]
[2, 2]
[3, 4, 1]
[5, 8, 3]
[8, 15, 8, 1]
[13, 28, 19, 4]

Diagonal:  [1, 1, 1, 1, 2, 2, 3, 4]

Polynomial values, array:

[1, 1, 1, 1, 1, 1, 1, 1]
[1, 2, 3, 4, 5, 6, 7, 8]
[1, 4, 9, 16, 25, 36, 49, 64]
[2, 10, 30, 68, 130, 222, 350, 520]
[3, 24, 99, 288, 675, 1368, 2499, 4224]
[5, 58, 327, 1220, 3505, 8430, 17843, 34312]
[8, 140, 1080, 5168, 18200, 51948, 127400, 278720]
[13, 338, 3567, 21892, 94505, 320118, 909643, 2264072]

Polynomial values, triangle:

[1]
[1, 1]
[1, 2, 1]
[2, 4, 3, 1]
[3, 10, 9, 4, 1]
[5, 24, 30, 16, 5, 1]
[8, 58, 99, 68, 25, 6, 1]
[13, 140, 327, 288, 130, 36, 7, 1]

PolyVal:  [1, 1, 1, 1, 2, 1, 2, 4]


=================
EulerianTriangle 

Triangle:  [1, 1, 0, 1, 1, 0, 1, 4]
Sum:       [1, 1, 2, 6, 24, 120, 720, 5040]
EvenSum:   [1, 1, 1, 2, 12, 68, 360, 2384]
OddSum:    [0, 0, 1, 4, 12, 52, 360, 2656]
AltSum:    [1, 1, 0, -2, 0, 16, 0, -272]
DiagSum:   [1, 1, 1, 2, 5, 13, 38, 125]
Central:   [1, 1, 11, 302]
LeftSide:  [1, 1, 1, 1, 1, 1, 1, 1]
RightSide: [1, 0, 0, 0, 0, 0, 0, 0]
PosHalf:   [1, 1, 3, 13, 75, 541, 4683, 47293]
NegHalf:   [1, 1, -1, -3, 15, 21, -441, 477]
N0TS:      [0, 0, 1, 6, 36, 240, 1800, 15120]
NATS:      [1, 1, 3, 12, 60, 360, 2520, 20160]


Triangle:

[1]
[1, 0]
[1, 1, 0]
[1, 4, 1, 0]
[1, 11, 11, 1, 0]
[1, 26, 66, 26, 1, 0]
[1, 57, 302, 302, 57, 1, 0]
[1, 120, 1191, 2416, 1191, 120, 1, 0]

Flat triangle:  [1, 1, 0, 1, 1, 0, 1, 4]

Inverse triangle:

Matrix not invertible


Diagonal triangle:

[1]
[1]
[1, 0]
[1, 1]
[1, 4, 0]
[1, 11, 1]
[1, 26, 11, 0]
[1, 57, 66, 1]

Diagonal:  [1, 1, 1, 0, 1, 1, 1, 4]

Polynomial values, array:

[1, 1, 1, 1, 1, 1, 1, 1]
[1, 1, 1, 1, 1, 1, 1, 1]
[1, 2, 3, 4, 5, 6, 7, 8]
[1, 6, 13, 22, 33, 46, 61, 78]
[1, 24, 75, 160, 285, 456, 679, 960]
[1, 120, 541, 1456, 3081, 5656, 9445, 14736]
[1, 720, 4683, 15904, 40005, 84336, 158095, 272448]
[1, 5040, 47293, 202672, 606033, 1467376, 3088765, 5881968]

Polynomial values, triangle:

[1]
[1, 1]
[1, 1, 1]
[1, 2, 1, 1]
[1, 6, 3, 1, 1]
[1, 24, 13, 4, 1, 1]
[1, 120, 75, 22, 5, 1, 1]
[1, 720, 541, 160, 33, 6, 1, 1]

PolyVal:  [1, 1, 1, 1, 1, 1, 1, 2]


The Laguerre triangle in different formats:

Triangle in standard format:

[1]
[1, 1]
[2, 4, 1]
[6, 18, 9, 1]
[24, 96, 72, 16, 1]
[120, 600, 600, 200, 25, 1]
[720, 4320, 5400, 2400, 450, 36, 1]

Triangle as a nested array:

Vector{Nemo.fmpz}[[1], [1, 1], [2, 4, 1], [6, 18, 9, 1], [24, 96, 72, 16, 1], [120, 600, 600, 200, 25, 1], [720, 4320, 5400, 2400, 450, 36, 1]]


Triangle in flattened format:



Triangle in info format with sequence ID:

[c85ebeb0] 1, 1, 1, 2, 4, 1, 6, 18, 9, 1, ... 

Triangle in mapped format:

0 ↦ 1
1 ↦ 1
2 ↦ 1
3 ↦ 2
4 ↦ 4
5 ↦ 1
6 ↦ 6
7 ↦ 18
8 ↦ 9
9 ↦ 1
10 ↦ 24
11 ↦ 96
12 ↦ 72
13 ↦ 16
14 ↦ 1
15 ↦ 120
16 ↦ 600
17 ↦ 600
18 ↦ 200
19 ↦ 25
20 ↦ 1
21 ↦ 720
22 ↦ 4320
23 ↦ 5400
24 ↦ 2400
25 ↦ 450
26 ↦ 36
27 ↦ 1
    Testing IntegerTriangles tests passed