A208201 -id:A208201 - cp's OEIS frontend

A208194 Number of n X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

1, 14, 10366, 156617480, 37069738362057, 136398703432330477549, 7801822458198433796561428608, 6937084083184530563330081968289999750, 95885498147917477608538934758547979039384601906

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Diagonal of A208201

			Some solutions for n=4
..0..1..0..0....0..0..0..0....0..0..0..1....0..0..1..0....0..0..1..2
..2..0..3..0....1..1..1..1....1..2..1..1....0..2..2..0....0..3..3..0
..2..0..3..1....2..1..2..3....0..2..0..3....2..3..3..0....1..0..1..2
..1..2..0..2....0..1..2..0....0..0..2..1....1..2..3..2....1..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..10

A208195 Number of n X 2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

Original entry on oeis.org

2, 14, 178, 2653, 41272, 648569, 10215440, 160984657, 2537249104, 39990174809, 630298266416, 9934351303777, 156578831693200, 2467894630281641, 38897365218137072, 613075213064694577, 9662896575843028048

Offset: 1

R. H. Hardin, Feb 24 2012

nonn

Column 2 of A208201.

			Some solutions for n=4:
..0..0....0..0....0..0....0..0....0..0....0..0....0..1....0..0....0..0....0..1
..0..1....1..0....1..1....1..0....1..0....0..1....1..1....0..1....0..1....1..0
..0..0....2..0....0..1....1..0....0..0....0..0....0..0....0..2....1..0....0..0
..1..2....1..2....0..0....0..1....0..1....0..2....0..1....1..3....2..2....2..0

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

Cf. A208201.

Empirical: a(n) = 18*a(n-1) - 31*a(n-2) - 66*a(n-3) - 24*a(n-4) for n>5.

Empirical g.f.: x*(2 - 22*x - 12*x^2 + 15*x^3 + 8*x^4) / ((1 - 3*x - 2*x^2)*(1 - 15*x - 12*x^2)). - Colin Barker, Jun 29 2018

A208196 Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

Original entry on oeis.org

5, 178, 10366, 639701, 39725054, 2468504665, 153402542384, 9533100532733, 592428713557570, 36816123505610549, 2287915709208554132, 142181136908012254369, 8835760693778126853518, 549093000211986917072609

Offset: 1

R. H. Hardin, Feb 24 2012

nonn

Column 3 of A208201.

			Some solutions for n=4:
..0..0..1....0..0..1....0..1..1....0..0..0....0..0..0....0..0..0....0..0..0
..0..2..0....0..1..0....1..0..2....0..1..0....0..1..2....0..1..0....0..1..2
..1..2..1....0..0..1....3..0..1....1..2..1....2..1..1....2..1..1....1..1..3
..3..0..0....1..1..0....1..1..1....0..1..3....0..1..2....0..2..1....1..0..0

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

Cf. A208201.

Empirical: a(n) = 66*a(n-1) - 222*a(n-2) - 1100*a(n-3) + 363*a(n-4) + 594*a(n-5) - 216*a(n-6) for n>7.

Empirical g.f.: x*(5 - 152*x - 272*x^2 + 561*x^3 + 25*x^4 - 261*x^5 + 72*x^6) / ((1 - 6*x - 3*x^2 + 2*x^3)*(1 - 60*x - 135*x^2 + 108*x^3)). - Colin Barker, Jun 29 2018

A208197 Number of nX4 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

Original entry on oeis.org

15, 2653, 639701, 156617480, 38372808893, 9402035642924, 2303673397508915, 564442821781056268, 138298988287411669755, 33885824084409470445384, 8302657077306720410135797, 2034305388933816797435987804

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 4 of A208201

			Some solutions for n=4
..0..0..0..1....0..0..0..1....0..1..1..0....0..0..0..1....0..0..0..0
..0..1..1..0....1..1..0..0....0..0..2..0....0..1..0..2....0..1..1..2
..0..1..2..3....2..3..3..0....0..2..1..1....2..1..0..3....1..0..1..3
..3..0..3..1....0..2..1..3....3..1..0..0....1..0..1..0....1..3..3..1

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

Empirical: a(n) = 236*a(n-1) +2368*a(n-2) -37526*a(n-3) -310734*a(n-4) +811712*a(n-5) +1791667*a(n-6) -2516274*a(n-7) -1895184*a(n-8) +2138400*a(n-9) -373248*a(n-10) for n>11

A208198 Number of nX5 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

Original entry on oeis.org

51, 41272, 39725054, 38372808893, 37069738362057, 35810971705853725, 34594950233928279876, 33420220819293699707599, 32285381308444124871905667, 31189077171790298063795540459, 30129999876244591484571731949842

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 5 of A208201

			Some solutions for n=4
..0..0..0..1..0....0..0..0..0..0....0..1..0..0..0....0..1..1..0..0
..0..1..1..0..2....0..1..0..2..0....1..0..0..1..0....0..2..0..0..2
..2..1..2..2..2....1..0..2..0..1....1..0..2..3..1....1..1..3..1..0
..0..1..3..1..3....2..1..3..0..0....3..2..2..1..1....0..1..0..2..3

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

Empirical: a(n) = 928*a(n-1) +38247*a(n-2) -1419908*a(n-3) -25003347*a(n-4) +1012531896*a(n-5) -9450054156*a(n-6) +24082844974*a(n-7) +80821917709*a(n-8) -489140400628*a(n-9) +403243304428*a(n-10) +1648713698424*a(n-11) -3331507779798*a(n-12) +632406681414*a(n-13) +2327643475767*a(n-14) -977046212844*a(n-15) -462110735853*a(n-16) +172474098336*a(n-17) +29511981612*a(n-18) -7270112880*a(n-19) for n>20

A208199 Number of nX6 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

Original entry on oeis.org

187, 648569, 2468504665, 9402035642924, 35810971705853725, 136398703432330477549, 519522527116810577984260, 1978784616446414312287693835, 7536898505819261464135073030914

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 6 of A208201

			Some solutions for n=4
..0..1..1..1..0..0....0..0..0..0..0..1....0..0..0..0..0..0....0..1..1..0..0..0
..0..1..0..1..0..1....0..1..2..1..3..2....0..1..1..0..2..1....0..1..2..3..2..1
..0..1..1..1..0..2....1..3..0..3..1..0....0..1..0..2..2..1....1..1..0..3..2..3
..3..0..1..2..1..1....2..1..0..3..3..3....0..3..1..0..1..0....3..0..0..2..1..3

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

A208200 Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

Original entry on oeis.org

715, 10215440, 153402542384, 2303673397508915, 34594950233928279876, 519522527116810577984260, 7801822458198433796561428608, 117162260457319989881048135168019, 1759460094015764611132758812387283596

Offset: 1

R. H. Hardin Feb 24 2012

nonn

Column 7 of A208201

			Some solutions for n=4
..0..0..0..1..0..1..0....0..1..2..3..0..1..2....0..0..0..0..0..0..0
..2..2..1..0..3..1..0....0..0..1..3..0..2..0....0..1..0..1..2..3..2
..1..0..0..0..1..2..0....3..0..2..0..3..1..1....2..0..2..1..0..1..2
..3..3..0..1..0..1..2....2..0..2..0..1..0..3....1..3..2..1..3..0..3

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

cp's OEIS Frontend

A208194 Number of n X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

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A208195 Number of n X 2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

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A208196 Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

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A208197 Number of nX4 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

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A208198 Number of nX5 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

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A208199 Number of nX6 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

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A208200 Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

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