A214906 -id:A214906 - cp's OEIS frontend

A214901 Number of nXnXn triangular 0..3 arrays with every horizontal row nondecreasing and having the same average value.

4, 6, 14, 50, 242, 1682, 13442, 134402, 1612802, 22579202, 361267202, 6864076802, 144145612802, 3459494707202, 93406357094402, 2802190712832002, 92472293523456002, 3421474860367872002, 136858994414714880002

Offset: 1

R. H. Hardin Jul 29 2012

nonn

Column 3 of A214906

			Some solutions for n=4
.....1........1........1........2........1........2........1........1
....1.1......1.1......0.2......2.2......0.2......2.2......0.2......1.1
...1.1.1....0.1.2....0.0.3....0.3.3....0.0.3....1.2.3....0.1.2....1.1.1
..0.1.1.2..0.1.1.2..0.1.1.2..0.2.3.3..1.1.1.1..0.2.3.3..0.0.2.2..0.0.2.2

R. H. Hardin, Table of n, a(n) for n = 1..89

A214902 Number of nXnXn triangular 0..4 arrays with every horizontal row nondecreasing and having the same average value.

Original entry on oeis.org

5, 9, 29, 182, 1802, 29162, 657722, 21063242, 892354322, 48771558002, 3355941877202, 288300261981602, 29970020819138402, 3775596638574103202, 566303743347081854402, 100233490058027413401602

Offset: 1

R. H. Hardin Jul 29 2012

nonn

Column 4 of A214906

			Some solutions for n=4
.....1........2........3........2........1........3........2........2
....1.1......0.4......2.4......2.2......0.2......3.3......1.3......0.4
...0.1.2....0.2.4....3.3.3....1.1.4....0.0.3....2.3.4....1.1.4....0.2.4
..0.0.0.4..0.2.3.3..0.4.4.4..1.1.2.4..1.1.1.1..1.3.4.4..0.1.3.4..1.2.2.3

R. H. Hardin, Table of n, a(n) for n = 1..120

A214903 Number of nXnXn triangular 0..5 arrays with every horizontal row nondecreasing and having the same average value.

Original entry on oeis.org

6, 12, 50, 458, 7550, 210914, 8943218, 560965610, 49301091506, 5963375071586, 960019298157026, 203519951213429090, 55357173186669891938, 19153563370287789473858, 8293491297187189536699650

Offset: 1

R. H. Hardin Jul 29 2012

nonn

Column 5 of A214906

			Some solutions for n=4
.....4........2........3........4........4........3........3........4
....4.4......0.4......2.4......3.5......3.5......3.3......1.5......3.5
...3.4.5....1.2.3....2.2.5....3.4.5....3.4.5....3.3.3....2.3.4....4.4.4
..4.4.4.4..0.0.3.5..2.3.3.4..3.4.4.5..3.3.5.5..1.3.4.4..3.3.3.3..3.3.5.5

R. H. Hardin, Table of n, a(n) for n = 1..107

A214904 Number of nXnXn triangular 0..6 arrays with every horizontal row nondecreasing and having the same average value.

Original entry on oeis.org

7, 16, 88, 1184, 31412, 1563440, 130431428, 17983769774, 3834925737542, 1241935634661854, 580437179573006186, 386026538656132081970, 351778685344619628965378, 434522760040678152959511554

Offset: 1

R. H. Hardin Jul 29 2012

nonn

Column 6 of A214906

			Some solutions for n=4
.....5........4........2........3........2........4........3........4
....4.6......3.5......2.2......0.6......0.4......3.5......2.4......4.4
...5.5.5....0.6.6....0.2.4....0.4.5....2.2.2....3.3.6....2.3.4....3.4.5
..4.5.5.6..2.4.5.5..1.1.3.3..0.3.4.5..1.1.2.4..0.4.6.6..1.1.5.5..2.4.4.6

R. H. Hardin, Table of n, a(n) for n = 1..90

A214905 Number of nXnXn triangular 0..7 arrays with every horizontal row nondecreasing and having the same average value.

Original entry on oeis.org

8, 20, 136, 2490, 100350, 8156190, 1207302502, 309961452102, 129904063711602, 85673347663408802, 85480932170854384802, 125968968872611859748002, 266580924247101550726536002, 795103957638983793244454088002

Offset: 1

R. H. Hardin Jul 29 2012

nonn

Column 7 of A214906

			Some solutions for n=4
.....3........5........3........3........2........5........3........4
....3.3......5.5......1.5......1.5......0.4......3.7......2.4......3.5
...0.4.5....1.7.7....0.3.6....0.3.6....0.3.3....5.5.5....1.4.4....1.4.7
..0.4.4.4..4.4.6.6..1.1.5.5..1.1.4.6..0.0.3.5..2.6.6.6..1.3.4.4..3.3.5.5

R. H. Hardin, Table of n, a(n) for n = 1..79

A214907 Number of 3 X 3 X 3 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.

Original entry on oeis.org

2, 6, 14, 29, 50, 88, 136, 209, 302, 430, 584, 793, 1034, 1344, 1704, 2149, 2652, 3270, 3956, 4777, 5690, 6760, 7934, 9305, 10792, 12502, 14360, 16469, 18740, 21312, 24062, 27145, 30444, 34110, 38010, 42337, 46916, 51960, 57302, 63149, 69314, 76054, 83134

Offset: 1

R. H. Hardin, Jul 29 2012

nonn

Row 3 of A214906.

			Some solutions for n=4:
....3......2......1......1......1......3......4......2......3......2......2
...3.3....2.2....0.2....1.1....0.2....2.4....4.4....1.3....2.4....0.4....0.4
..1.4.4..1.2.3..0.1.2..0.1.2..0.0.3..2.3.4..4.4.4..1.2.3..3.3.3..1.1.4..0.3.3

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A214906.

Empirical: a(n) = 2*a(n-2) + 2*a(n-3) - 4*a(n-5) - 3*a(n-6) + 3*a(n-8) + 4*a(n-9) - 2*a(n-11) - 2*a(n-12) + a(n-14).

G.f.: x*(2 + 6*x + 10*x^2 + 13*x^3 + 10*x^4 + 10*x^5 + 8*x^6 + 7*x^7 + 6*x^8 + x^9 - 2*x^10 - 2*x^11 + x^13) / ((1 - x)^5*(1 + x)^3*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, Jul 22 2018

A214908 Number of 4X4X4 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.

Original entry on oeis.org

2, 14, 50, 182, 458, 1184, 2490, 5213, 9722, 17864, 30284, 51088, 80840, 127040, 191162, 285357, 410940, 589294, 820180, 1136378, 1538406, 2072864, 2738172, 3606249, 4667108, 6021672, 7659902, 9714004, 12163526, 15197912, 18774496

Offset: 1

R. H. Hardin Jul 29 2012

nonn

Row 4 of A214906

			Some solutions for n=4
.....2........2........2........2........3........2........2........2
....2.2......1.3......1.3......2.2......2.4......1.3......1.3......0.4
...1.1.4....1.2.3....0.3.3....2.2.2....2.3.4....1.2.3....0.3.3....0.2.4
..1.1.3.3..1.1.3.3..0.1.3.4..0.1.3.4..1.3.4.4..0.2.2.4..2.2.2.2..1.2.2.3

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = a(n-4) +2*a(n-6) +2*a(n-8) +2*a(n-9) -2*a(n-10) -2*a(n-12) -2*a(n-13) -4*a(n-14) -4*a(n-15) -a(n-16) -4*a(n-17) +a(n-18) +4*a(n-19) +a(n-20) +4*a(n-21) +5*a(n-22) +8*a(n-23) +3*a(n-24) +2*a(n-25) +4*a(n-26) -4*a(n-27) -3*a(n-28) -2*a(n-29) -6*a(n-30) -8*a(n-31) -6*a(n-32) -2*a(n-33) -3*a(n-34) -4*a(n-35) +4*a(n-36) +2*a(n-37) +3*a(n-38) +8*a(n-39) +5*a(n-40) +4*a(n-41) +a(n-42) +4*a(n-43) +a(n-44) -4*a(n-45) -a(n-46) -4*a(n-47) -4*a(n-48) -2*a(n-49) -2*a(n-50) -2*a(n-52) +2*a(n-53) +2*a(n-54) +2*a(n-56) +a(n-58) -a(n-62)

A214909 Number of 5X5X5 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.

Original entry on oeis.org

2, 38, 242, 1802, 7550, 31412, 100350, 310079, 811472, 2065406, 4695974, 10458806, 21370898, 42897546, 80938346, 150245395, 265231474, 462690716, 774729470, 1283610082, 2057355212, 3266479406, 5043183866, 7727895633, 11557992252

Offset: 1

R. H. Hardin Jul 29 2012

nonn

Row 5 of A214906

			Some solutions for n=4
......2..........2..........2..........2..........2..........2..........2
.....2.2........1.3........2.2........1.3........2.2........2.2........1.3
....2.2.2......0.3.3......1.2.3......1.1.4......2.2.2......1.1.4......1.2.3
...1.1.3.3....1.1.3.3....0.1.3.4....1.1.3.3....0.2.3.3....0.1.3.4....0.2.2.4
..1.1.2.3.3..0.1.2.3.4..0.0.2.4.4..1.2.2.2.3..0.2.2.3.3..1.1.2.3.3..0.1.1.4.4

R. H. Hardin, Table of n, a(n) for n = 1..210

A214910 Number of 6X6X6 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.

Original entry on oeis.org

2, 146, 1682, 29162, 210914, 1563440, 8156190, 40258709, 158198222, 595338230, 1928269526, 6018440390, 16759097486, 45277885958, 112522145318, 272384422903, 616484632830, 1366517073926, 2868519969642, 5914643033078, 11661558993698

Offset: 1

R. H. Hardin Jul 29 2012

nonn

Row 6 of A214906

			Some solutions for n=4
.......2............2............2............2............3............1
......2.2..........1.3..........0.4..........1.3..........2.4..........0.2
.....1.1.4........0.3.3........1.2.3........1.2.3........2.3.4........1.1.1
....0.1.3.4......2.2.2.2......0.1.3.4......1.2.2.3......0.4.4.4......0.1.1.2
...0.1.3.3.3....2.2.2.2.2....2.2.2.2.2....0.1.1.4.4....1.3.3.4.4....0.0.1.2.2
..0.1.1.3.3.4..2.2.2.2.2.2..0.0.2.2.4.4..0.0.2.2.4.4..1.2.3.4.4.4..0.0.0.2.2.2

R. H. Hardin, Table of n, a(n) for n = 1..210

A214911 Number of 7X7X7 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.

Original entry on oeis.org

2, 578, 13442, 657722, 8943218, 130431428, 1207302502, 10272615125, 64849263302, 384014075750, 1885027008818, 8723067515222, 34924262211422, 133490468673758, 458639082931598, 1515242313469477, 4594326578653430, 13491494779735190

Offset: 1

R. H. Hardin Jul 29 2012

nonn

Row 7 of A214906

			Some solutions for n=4
........2..............2..............2..............2..............2
.......0.4............0.4............0.4............0.4............0.4
......1.1.4..........1.1.4..........0.2.4..........1.1.4..........1.1.4
.....2.2.2.2........0.2.3.3........2.2.2.2........0.2.3.3........1.2.2.3
....0.2.2.3.3......0.2.2.3.3......1.1.2.3.3......0.0.3.3.4......0.1.3.3.3
...2.2.2.2.2.2....0.0.2.3.3.4....0.2.2.2.2.4....0.2.2.2.3.3....0.1.1.3.3.4
..0.1.2.2.3.3.3..1.1.1.1.2.4.4..0.1.1.2.2.4.4..0.0.2.2.3.3.4..0.1.1.1.3.4.4

R. H. Hardin, Table of n, a(n) for n = 1..210

cp's OEIS Frontend

A214901 Number of nXnXn triangular 0..3 arrays with every horizontal row nondecreasing and having the same average value.

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A214902 Number of nXnXn triangular 0..4 arrays with every horizontal row nondecreasing and having the same average value.

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A214903 Number of nXnXn triangular 0..5 arrays with every horizontal row nondecreasing and having the same average value.

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A214904 Number of nXnXn triangular 0..6 arrays with every horizontal row nondecreasing and having the same average value.

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A214905 Number of nXnXn triangular 0..7 arrays with every horizontal row nondecreasing and having the same average value.

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A214907 Number of 3 X 3 X 3 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.

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A214908 Number of 4X4X4 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.

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A214909 Number of 5X5X5 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.

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A214910 Number of 6X6X6 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.

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A214911 Number of 7X7X7 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.

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