A214352 -id:A214352 - cp's OEIS frontend

A214353 Number of 3 X 3 X 3 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

26, 169, 660, 1951, 4822, 10507, 20840, 38421, 66802, 110693, 176188, 271011, 404782, 589303, 838864, 1170569, 1604682, 2164993, 2879204, 3779335, 4902150, 6289603, 7989304, 10055005, 12547106, 15533181, 19088524, 23296715, 28250206

Offset: 1

R. H. Hardin, Jul 13 2012

nonn

Row 3 of A214352.

			Some solutions for n=3:
....1......1......2......1......2......1......3......2......3......2......0
...2.0....1.1....2.1....1.1....2.2....1.2....3.1....0.3....0.3....1.3....1.0
..3.2.0..0.3.1..3.1.3..0.3.0..2.2.0..2.1.2..3.1.0..0.3.2..0.1.3..1.2.3..3.1.0

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

Cf. A214352.

Empirical: a(n) = (1/36)*n^6 + (7/15)*n^5 + (25/9)*n^4 + (15/2)*n^3 + (331/36)*n^2 + (151/30)*n + 1.
Conjectures from Colin Barker, Jul 22 2018: (Start)
G.f.: x*(26 - 13*x + 23*x^2 - 30*x^3 + 20*x^4 - 7*x^5 + x^6) / (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)

A214354 Number of 4X4X4 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

Original entry on oeis.org

160, 2853, 23554, 127813, 529006, 1807653, 5349708, 14150061, 34190300, 76678305, 161533230, 322614617, 615330522, 1127418361, 1993875448, 3417225641, 5694545880, 9252943437, 14695473146, 22859815485, 34892402886, 52341084797

Offset: 1

R. H. Hardin Jul 13 2012

nonn

Row 4 of A214352

			Some solutions for n=3
.....2........2........1........2........0........2........2........1
....2.2......3.1......0.3......2.1......0.0......3.2......2.1......1.2
...3.0.2....3.1.2....0.0.3....2.1.2....0.0.0....1.3.0....3.1.3....0.2.2
..3.0.2.1..3.0.2.1..0.0.3.1..3.0.2.2..1.0.0.3..1.3.0.1..3.0.3.1..0.1.3.2

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

Empirical: a(n) = (109/226800)*n^10 + (1531/90720)*n^9 + (1471/6048)*n^8 + (28627/15120)*n^7 + (47321/5400)*n^6 + (107767/4320)*n^5 + (789913/18144)*n^4 + (127789/2835)*n^3 + (111121/4200)*n^2 + (5083/630)*n + 1

A214355 Number of 5X5X5 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

Original entry on oeis.org

1386, 80573, 1602092, 17790765, 135538054, 790197579, 3766437036, 15329961031, 54922753470, 177082458729, 522464071332, 1428914669655, 3659885495134, 8851607656183, 20351858523224, 44735107468453, 94449669596498

Offset: 1

R. H. Hardin Jul 13 2012

nonn

Row 5 of A214352

			Some solutions for n=2
......2..........2..........1..........1..........2..........1..........1
.....2.1........1.2........1.2........0.2........2.1........2.0........1.0
....2.2.1......0.2.1......1.2.2......0.1.2......2.1.0......2.2.0......2.1.0
...0.2.0.2....0.2.0.2....1.2.2.2....1.0.2.1....2.1.0.1....2.2.0.2....0.2.0.1
..1.0.2.0.2..0.1.2.0.2..1.2.2.2.1..0.1.0.2.1..2.0.2.0.1..2.2.0.1.2..1.0.2.0.1

R. H. Hardin, Table of n, a(n) for n = 1..64

Empirical: a(n) = (250321/163459296000)*n^15 + (57931/605404800)*n^14 + (6130183/2335132800)*n^13 + (5021701/119750400)*n^12 + (12225673/28066500)*n^11 + (33845911/10886400)*n^10 + (1793738911/114307200)*n^9 + (1441174417/25401600)*n^8 + (3431403169/23328000)*n^7 + (2949422359/10886400)*n^6 + (31221432373/89812800)*n^5 + (4515147647/14968800)*n^4 + (193448384201/1135134000)*n^3 + (4506398063/75675600)*n^2 + (2113313/180180)*n + 1

A214356 Number of 6X6X6 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

Original entry on oeis.org

16814, 3778867, 205613460, 5193620491, 79817831414, 861351043995, 7118347901224, 47699363705707, 269726763260946, 1325185747304093, 5782740500683900, 22798874223531873, 82318717666693690, 275194896097342957

Offset: 1

R. H. Hardin Jul 13 2012

nonn

Row 6 of A214352

			Some solutions for n=1
.......0............0............1............0............1............0
......0.0..........0.0..........1.0..........0.0..........0.1..........1.0
.....0.0.1........0.0.0........1.0.0........1.0.0........0.1.0........1.0.0
....1.0.1.1......1.0.0.1......1.0.0.0......0.1.0.0......0.1.0.0......1.1.0.0
...0.1.0.1.0....1.0.0.1.1....0.1.0.0.0....1.0.1.0.1....0.1.1.0.1....0.1.1.0.0
..0.1.0.0.1.0..1.1.0.0.1.0..1.0.1.0.0.1..1.0.0.1.0.1..0.0.1.1.0.1..0.1.1.0.1.0

R. H. Hardin, Table of n, a(n) for n = 1..19

A214357 Number of 7X7X7 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

Original entry on oeis.org

284724, 293207907, 49555044358, 3160001994563, 107180513854464, 2318511875463567, 35699489509054494, 420636918387554285, 3989623026879608554, 31608512602702469537, 215115456420213959696

Offset: 1

R. H. Hardin Jul 13 2012

nonn

Row 7 of A214352

			Some solutions for n=1
........0..............0..............0..............0..............0
.......0.1............0.0............0.0............0.1............0.0
......0.1.0..........0.0.0..........0.0.0..........0.1.1..........1.0.0
.....0.1.0.0........1.0.1.0........0.1.0.1........0.0.1.1........1.1.0.1
....0.0.1.0.0......1.0.1.1.0......0.1.1.0.1......0.0.1.1.0......1.1.0.0.1
...1.0.1.0.0.1....1.1.0.1.1.0....0.1.1.0.1.1....1.0.1.1.0.0....1.1.0.0.1.1
..0.1.0.1.0.1.0..1.1.0.0.1.0.0..0.0.1.0.1.0.1..1.0.1.0.1.0.0..0.1.0.1.0.1.1

R. H. Hardin, Table of n, a(n) for n = 1..13

A214346 Number of nXnXn triangular 0..2 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

Original entry on oeis.org

3, 17, 169, 2853, 80573, 3778867, 293207907, 37563586269, 7937469117891, 2764964877941141, 1587376056676684453, 1501785457780559131093, 2341332949071519298798233

Offset: 1

R. H. Hardin Jul 13 2012

nonn

Column 2 of A214352

			Some solutions for n=3
....2......2......0......1......1......1......1......0......0......2......1
...0.2....2.1....0.2....1.1....1.1....2.1....2.0....2.0....0.1....0.2....1.2
..0.2.1..2.0.1..0.2.2..1.0.1..0.2.1..2.2.1..1.2.0..2.2.0..0.0.2..2.0.2..0.1.2

A214347 Number of nXnXn triangular 0..3 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

Original entry on oeis.org

4, 36, 660, 23554, 1602092, 205613460, 49555044358, 22380167899116, 18924317057007778, 29956465204908956664, 88786379727557659524194

Offset: 1

R. H. Hardin Jul 13 2012

nonn

Column 3 of A214352

			Some solutions for n=3
....0......1......1......0......0......1......2......1......3......2......3
...0.1....3.1....1.2....1.0....1.0....0.3....2.1....3.1....3.2....2.1....3.1
..0.0.3..3.2.1..1.0.2..1.2.0..1.0.1..0.3.3..1.3.1..3.0.2..2.3.0..3.2.0..3.0.2

A214348 Number of nXnXn triangular 0..4 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

Original entry on oeis.org

5, 65, 1951, 127813, 17790765, 5193620491, 3160001994563, 3995872591050989, 10489950826300197841, 57160724000127089232531

Offset: 1

R. H. Hardin Jul 13 2012

nonn

Column 4 of A214352

			Some solutions for n=3
....4......2......1......1......3......1......1......1......2......1......1
...0.4....1.2....1.4....4.1....3.0....2.1....2.0....0.4....2.2....1.3....0.2
..1.0.4..1.3.2..1.4.4..4.4.0..4.3.0..2.2.1..4.0.1..4.0.4..4.0.2..1.1.4..0.1.2

A214349 Number of nXnXn triangular 0..5 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

Original entry on oeis.org

6, 106, 4822, 529006, 135538054, 79817831414, 107180513854464, 326914413025767444, 2261157562438763862818

Offset: 1

R. H. Hardin Jul 13 2012

nonn

Column 5 of A214352

			Some solutions for n=3
....1......2......4......3......1......5......0......2......1......1......4
...4.1....2.2....5.2....5.2....4.1....5.3....0.3....3.0....2.1....2.1....4.1
..0.5.1..3.2.1..3.5.0..5.2.3..3.5.0..5.4.3..1.0.5..3.0.4..4.2.1..0.4.0..5.4.0

A214350 Number of nXnXn triangular 0..6 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

Original entry on oeis.org

7, 161, 10507, 1807653, 790197579, 861351043995, 2318511875463567, 15333331066778365463

Offset: 1

R. H. Hardin Jul 13 2012

nonn

Column 6 of A214352

			Some solutions for n=3
....2......3......3......3......4......4......3......3......2......2......6
...6.1....1.4....4.1....3.4....4.1....2.4....1.5....3.1....2.0....2.5....5.6
..2.6.1..5.0.4..6.1.0..3.6.4..4.3.0..3.2.5..1.6.0..4.1.2..5.0.0..2.5.0..3.6.0

cp's OEIS Frontend

A214353 Number of 3 X 3 X 3 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

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A214354 Number of 4X4X4 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

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A214355 Number of 5X5X5 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

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A214356 Number of 6X6X6 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

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A214357 Number of 7X7X7 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

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A214346 Number of nXnXn triangular 0..2 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

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A214347 Number of nXnXn triangular 0..3 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

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A214348 Number of nXnXn triangular 0..4 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

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A214349 Number of nXnXn triangular 0..5 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

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A214350 Number of nXnXn triangular 0..6 arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors.

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