A271034 -id:A271034 - cp's OEIS frontend

A271028 Number of nXnXn triangular 0..2 arrays with some element less than a w, nw or ne neighbor exactly once.

0, 8, 72, 450, 2420, 12010, 56754, 259628, 1160936, 5105144, 22166760, 95301932, 406510934, 1722863088, 7263024536, 30481913682, 127442700854, 531088604958, 2206913662766, 9147940180122, 37836235984334, 156187232759706

Offset: 1

R. H. Hardin, Mar 29 2016

nonn

Column 2 of A271034.

			Some solutions for n=4
.....0........1........0........0........1........2........0........0
....0.0......1.1......0.1......0.0......1.1......2.2......1.2......0.2
...0.0.0....1.1.2....1.1.1....2.0.1....0.1.1....0.2.2....2.2.2....0.2.2
..0.2.2.1..0.2.2.2..0.1.1.1..2.2.2.2..0.1.1.1..0.2.2.2..0.2.2.2..0.1.2.2

R. H. Hardin, Table of n, a(n) for n = 1..30

Cf. A271034.

A271029 Number of nXnXn triangular 0..3 arrays with some element less than a w, nw or ne neighbor exactly once.

Original entry on oeis.org

0, 20, 294, 3114, 29120, 256020, 2173554, 18060096, 147976270, 1201034302, 9684108034, 77719446198, 621623562780, 4959585660212, 39496945637162, 314112558505488, 2495519478658458, 19810840820555514, 157179628657888198

Offset: 1

R. H. Hardin, Mar 29 2016

nonn

Column 3 of A271034.

			Some solutions for n=4
.....3........0........0........1........1........0........0........0
....0.3......0.2......0.0......1.1......1.1......0.2......0.2......1.0
...0.3.3....1.3.3....0.0.1....1.3.2....0.2.2....0.2.2....1.2.2....1.3.3
..0.3.3.3..1.2.3.3..2.1.1.3..1.3.3.3..1.2.2.3..1.1.2.3..2.3.2.2..3.3.3.3

R. H. Hardin, Table of n, a(n) for n = 1..20

Cf. A271034.

A271035 Number of 3 X 3 X 3 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.

Original entry on oeis.org

10, 72, 294, 896, 2268, 5040, 10164, 19008, 33462, 56056, 90090, 139776, 210392, 308448, 441864, 620160, 854658, 1158696, 1547854, 2040192, 2656500, 3420560, 4359420, 5503680, 6887790, 8550360, 10534482, 12888064, 15664176, 18921408

Offset: 1

R. H. Hardin, Mar 29 2016

nonn

			Some solutions for n=4:
....1......4......0......3......0......0......0......1......3......1......0
...0.1....2.4....2.4....0.4....2.1....0.0....0.0....0.2....0.3....1.1....2.2
..3.3.3..4.4.4..1.4.4..3.4.4..2.2.2..2.2.1..2.3.0..1.3.4..3.3.3..0.2.2..4.2.2

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

Row 3 of A271034.

Empirical: a(n) = (1/60)*n^6 + (7/30)*n^5 + (5/4)*n^4 + (19/6)*n^3 + (56/15)*n^2 + (8/5)*n.
Conjectures from Colin Barker, Jan 30 2019: (Start)
G.f.: 2*x*(5 + x) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A271036 Number of 4 X 4 X 4 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.

Original entry on oeis.org

34, 450, 3114, 15116, 58036, 188034, 535106, 1373944, 3244098, 7143708, 14829100, 29262168, 55258840, 100405196, 176323116, 300384832, 497995586, 805585902, 1274479910, 1975833860, 3006869580, 4498661310, 6625771230, 9618069240

Offset: 1

R. H. Hardin, Mar 29 2016

nonn

			Some solutions for n=4:
.....0........2........2........0........0........0........1........1
....0.1......2.3......2.3......0.0......1.0......0.0......1.1......1.1
...1.2.1....1.3.3....2.3.3....0.2.1....2.3.4....0.0.1....1.1.1....0.1.2
..1.3.3.4..4.4.4.4..4.4.4.3..3.3.3.4..4.4.4.4..3.4.3.4..0.3.3.4..2.2.3.4

R. H. Hardin, Table of n, a(n) for n = 1..96

Row 4 of A271034.

Empirical: a(n) = (73/1814400)*n^10 + (169/120960)*n^9 + (1277/60480)*n^8 + (3667/20160)*n^7 + (84829/86400)*n^6 + (3953/1152)*n^5 + (87629/11340)*n^4 + (324707/30240)*n^3 + (104197/12600)*n^2 + (278/105)*n.
Conjectures from Colin Barker, Jan 30 2019: (Start)
G.f.: 2*x*(17 + 38*x + 17*x^2 + x^3) / (1 - x)^11.
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
(End)

A271037 Number of 5X5X5 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.

Original entry on oeis.org

98, 2420, 29120, 232432, 1402082, 6872424, 28658242, 104918592, 344970188, 1036183048, 2880940360, 7491977248, 18376721948, 42808972960, 95252409300, 203411012288, 418599114270, 833032325020, 1607950467240, 3018338301840

Offset: 1

R. H. Hardin, Mar 29 2016

nonn

Row 5 of A271034.

			Some solutions for n=3
......0..........0..........0..........0..........0..........1..........0
.....0.1........0.1........0.1........1.1........0.0........1.1........0.0
....1.1.1......0.3.3......0.1.1......1.2.2......0.1.1......1.2.2......1.1.1
...1.1.2.2....0.0.3.3....0.1.2.1....0.2.2.2....0.1.1.1....2.2.2.2....1.2.2.1
..1.3.3.2.3..2.3.3.3.3..0.2.2.2.2..3.3.3.3.3..3.2.3.3.3..2.2.3.2.2..2.2.3.3.3

R. H. Hardin, Table of n, a(n) for n = 1..43

Cf. A271034.

Empirical: a(n) = (271/59439744000)*n^15 + (13547/43589145600)*n^14 + (13957/1437004800)*n^13 + (88289/479001600)*n^12 + (17036507/7185024000)*n^11 + (190313/8709120)*n^10 + (135902587/914457600)*n^9 + (230644919/304819200)*n^8 + (134986897/46656000)*n^7 + (89816651/10886400)*n^6 + (281267579/16329600)*n^5 + (23798177/935550)*n^4 + (394130917/15765750)*n^3 + (137477173/9459450)*n^2 + (12932/3465)*n

A271038 Number of 6X6X6 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.

Original entry on oeis.org

258, 12010, 256020, 3441072, 33505396, 255757328, 1610555756, 8669119882, 40937078274, 172973004078, 664139482668, 2345904959628, 7699860067962, 23679297338148, 68702482342180, 189162014324890, 496732138963680

Offset: 1

R. H. Hardin, Mar 29 2016

nonn

Row 6 of A271034.

			Some solutions for n=2
.......0............0............0............0............0............0
......0.0..........0.0..........0.0..........0.1..........0.0..........0.2
.....0.0.0........0.0.1........0.0.0........0.1.1........0.0.0........0.2.2
....0.0.0.1......1.0.1.1......0.0.0.0......0.1.1.1......0.0.0.1......0.0.2.2
...1.1.0.1.1....1.1.2.2.2....1.1.1.1.1....0.2.2.2.1....0.0.1.1.2....1.2.2.2.2
..1.1.1.2.2.2..1.1.2.2.2.2..2.2.1.1.2.2..1.2.2.2.2.2..1.1.1.1.1.2..1.2.2.2.2.2

R. H. Hardin, Table of n, a(n) for n = 1..26

Cf. A271034.

Empirical: a(n) = (3307/154821036883968000)*n^21 + (277057/110586454917120000)*n^20 + (1603411/11585247657984000)*n^19 + (2270033/474249904128000)*n^18 + (30996697/266765571072000)*n^17 + (101572363/48283361280000)*n^16 + (77666311187/2636271525888000)*n^15 + (123014962363/376610217984000)*n^14 + (11598452441/3985293312000)*n^13 + (2030854507051/96566722560000)*n^12 + (2391727070743/19313344512000)*n^11 + (1044262844011/1755758592000)*n^10 + (1225063692125929/527254305177600)*n^9 + (35232199804051/4803701760000)*n^8 + (1481084911939/80061696000)*n^7 + (575071748810329/15692092416000)*n^6 + (2470455323050879/44460928512000)*n^5 + (9812842428469/158336640000)*n^4 + (1957326271199891/41064607584000)*n^3 + (2192821336711/97772875200)*n^2 + (37411763/7759752)*n

A271039 Number of 7X7X7 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.

Original entry on oeis.org

642, 56754, 2173554, 50108414, 804566180, 9790184488, 95420380090, 774600507974, 5391017644856, 32890239598008, 179007489630476, 881467345491584, 3972721376352724, 16545720243662726, 64195774252619306

Offset: 1

R. H. Hardin, Mar 29 2016

nonn

Row 7 of A271034.

			Some solutions for n=2
........0..............0..............0..............0..............0
.......0.0............0.0............0.0............0.1............0.0
......0.0.0..........0.2.2..........0.1.1..........0.1.1..........0.0.0
.....0.0.1.0........1.1.2.2........0.1.1.1........0.0.2.2........0.0.1.1
....0.1.1.1.2......1.1.2.2.2......1.1.2.1.2......0.0.2.2.2......1.1.1.1.1
...0.1.1.1.2.2....1.1.2.2.2.2....2.2.2.2.2.2....0.1.2.2.2.2....0.1.1.1.1.1
..0.2.2.2.2.2.2..1.1.2.2.2.2.2..2.2.2.2.2.2.2..0.1.2.2.2.2.2..1.2.2.2.2.2.2

R. H. Hardin, Table of n, a(n) for n = 1..18

Cf. A271034.

A271030 Number of nXnXn triangular 0..4 arrays with some element less than a w, nw or ne neighbor exactly once.

Original entry on oeis.org

0, 40, 896, 15116, 232432, 3441072, 50108414, 724727082, 10461499634, 151103449566, 2186779416368, 31731721875678, 461837305110082, 6742912667242640, 98757904224890770, 1450886824492563414

Offset: 1

R. H. Hardin, Mar 29 2016

nonn

Column 4 of A271034.

			Some solutions for n=4
.....0........2........0........0........0........1........2........0
....0.0......2.4......0.1......0.0......0.2......1.4......0.2......0.0
...0.2.3....0.4.4....1.1.1....1.1.2....3.3.3....1.2.4....0.2.4....2.3.0
..2.4.3.4..0.4.4.4..2.3.1.3..3.1.3.4..4.3.3.3..2.3.4.4..0.4.4.4..2.3.4.4

Cf. A271034.

A271031 Number of nXnXn triangular 0..5 arrays with some element less than a w, nw or ne neighbor exactly once.

Original entry on oeis.org

0, 70, 2268, 58036, 1402082, 33505396, 804566180, 19525545192, 479803630966, 11941873574498, 300926010716524, 7672376906432844, 197762508822690802

Offset: 1

R. H. Hardin, Mar 29 2016

nonn

Column 5 of A271034.

			Some solutions for n=4
.....1........1........0........0........1........0........0........2
....0.1......1.2......1.2......3.3......1.1......0.4......1.1......0.2
...0.2.2....0.3.4....1.2.4....0.3.3....1.1.2....4.4.4....3.5.5....0.2.3
..3.3.3.4..3.3.5.5..2.2.5.4..0.3.5.5..3.2.3.4..5.5.4.5..1.5.5.5..1.2.4.5

Cf. A271034.

A271032 Number of n X n X n triangular 0..6 arrays with some element less than a w, nw or ne neighbor exactly once.

Original entry on oeis.org

0, 112, 5040, 188034, 6872424, 255757328, 9790184488, 386105784866, 15669594394610, 653037680536962, 27884254995169022, 1217213333853178756

Offset: 1

R. H. Hardin, Mar 29 2016

nonn

Column 6 of A271034.

			Some solutions for n=4
.....0........0........1........1........1........1........1........0
....0.1......2.2......0.2......1.1......1.1......0.2......1.2......0.0
...1.4.5....2.3.4....0.2.2....2.2.5....3.5.5....2.2.2....1.2.2....0.0.4
..1.2.5.5..5.3.4.4..4.4.4.5..6.6.6.5..2.5.5.5..6.6.6.6..3.3.2.3..4.4.5.4

Cf. A271034.

cp's OEIS Frontend

A271028 Number of nXnXn triangular 0..2 arrays with some element less than a w, nw or ne neighbor exactly once.

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A271029 Number of nXnXn triangular 0..3 arrays with some element less than a w, nw or ne neighbor exactly once.

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A271035 Number of 3 X 3 X 3 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.

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A271036 Number of 4 X 4 X 4 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.

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A271037 Number of 5X5X5 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.

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A271038 Number of 6X6X6 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.

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A271039 Number of 7X7X7 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.

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A271030 Number of nXnXn triangular 0..4 arrays with some element less than a w, nw or ne neighbor exactly once.

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A271031 Number of nXnXn triangular 0..5 arrays with some element less than a w, nw or ne neighbor exactly once.

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A271032 Number of n X n X n triangular 0..6 arrays with some element less than a w, nw or ne neighbor exactly once.

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