A295918 -id:A295918 - cp's OEIS frontend

A295913 Number of n X 3 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1's.

5, 13, 39, 115, 337, 993, 2919, 8587, 25257, 74289, 218511, 642715, 1890449, 5560465, 16355255, 48106475, 141497817, 416194129, 1224171199, 3600711835, 10590941633, 31151630513, 91627743527, 269508954923, 792719257161, 2331662118065

Offset: 1

R. H. Hardin, Nov 29 2017

nonn

			Some solutions for n=7:
..0..0..1. .1..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..1..1
..0..0..0. .0..0..0. .0..1..1. .0..0..0. .0..0..0. .1..0..1. .0..1..1
..0..1..0. .0..0..0. .0..1..1. .1..0..1. .0..1..1. .0..0..0. .0..0..0
..0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..1..1. .0..0..0. .1..0..1
..0..0..0. .1..1..0. .0..0..0. .0..0..0. .0..0..0. .1..0..0. .0..0..0
..0..0..0. .1..1..0. .0..0..0. .1..0..0. .1..0..0. .0..0..0. .0..0..0
..1..0..0. .0..0..0. .0..0..1. .0..0..1. .0..0..1. .0..0..1. .0..0..0

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

Column 3 of A295918.

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-4).

Empirical g.f.: x*(5 + 3*x - 2*x^2 - 2*x^3) / (1 - 2*x - 3*x^2 + 2*x^4). - Colin Barker, Feb 22 2019

A295914 Number of n X 4 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1s.

Original entry on oeis.org

8, 28, 115, 467, 1880, 7604, 30721, 124117, 501512, 2026304, 8187195, 33079959, 133657824, 540037688, 2181994609, 8816237625, 35621557528, 143927081684, 581530015059, 2349642293451, 9493609553944, 38358444014860, 154985331853649

Offset: 1

R. H. Hardin, Nov 29 2017

nonn

			Some solutions for n=7:
..1..0..0..0. .0..1..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..1
..0..0..1..0. .0..0..0..0. .1..0..0..0. .1..0..0..0. .1..1..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..0. .1..1..0..0
..1..1..0..0. .0..0..0..0. .0..1..0..1. .0..0..0..0. .0..0..0..1
..1..1..0..0. .0..0..1..0. .0..0..0..0. .0..0..0..0. .1..0..0..0
..0..0..0..1. .1..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..1..0. .0..0..0..0. .0..0..0..1. .0..1..0..0

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

Column 4 of A295918.

Empirical: a(n) = 2*a(n-1) + 7*a(n-2) + 6*a(n-3) - 3*a(n-4) - 4*a(n-5) + a(n-6).

Empirical g.f.: x*(8 + 12*x + 3*x^2 - 7*x^3 - 3*x^4 + x^5) / ((1 + x)*(1 - 3*x - 4*x^2 - 2*x^3 + 5*x^4 - x^5)). - Colin Barker, Feb 22 2019

A295915 Number of nX5 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1s.

Original entry on oeis.org

13, 60, 337, 1880, 10290, 56955, 314044, 1732883, 9562608, 52762665, 291142893, 1606482609, 8864368984, 48912478517, 269892775507, 1489234149184, 8217404544373, 45342593611494, 250194667755280, 1380542367891973

Offset: 1

R. H. Hardin, Nov 29 2017

nonn

Column 5 of A295918.

			Some solutions for n=6
..0..0..0..0..0. .0..0..0..0..1. .0..1..0..1..0. .0..0..0..0..0
..0..0..0..0..1. .1..0..0..0..0. .0..0..0..0..0. .1..0..1..0..1
..0..0..1..0..0. .0..0..1..0..1. .0..0..0..0..1. .0..0..0..0..0
..0..0..0..0..0. .1..0..0..0..0. .0..0..1..0..0. .1..0..1..0..0
..0..0..1..0..0. .0..0..0..0..1. .0..0..0..0..0. .0..0..0..0..1
..1..0..0..0..0. .0..0..1..0..0. .0..0..0..0..0. .0..0..1..0..0

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

Cf. A295918.

Empirical: a(n) = 3*a(n-1) +15*a(n-2) +102*a(n-3) -342*a(n-4) -1512*a(n-5) -3295*a(n-6) +13427*a(n-7) +47860*a(n-8) +42567*a(n-9) -240345*a(n-10) -621149*a(n-11) -140019*a(n-12) +1975855*a(n-13) +3017471*a(n-14) -1228175*a(n-15) -5445207*a(n-16) -1693493*a(n-17) +6520443*a(n-18) -6122855*a(n-19) -3746602*a(n-20) +5507184*a(n-21) +2158920*a(n-22) +5052409*a(n-23) -2505685*a(n-24) -15612775*a(n-25) -6104943*a(n-26) +16537300*a(n-27) -1244574*a(n-28) -2319152*a(n-29) -483988*a(n-30) +1004084*a(n-31) -258602*a(n-32) -120112*a(n-33) +129320*a(n-34) +67468*a(n-35) +4144*a(n-36) -21040*a(n-37) -4240*a(n-38)

A295916 Number of nX6 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1s.

Original entry on oeis.org

21, 129, 993, 7604, 56955, 431844, 3261576, 24650278, 186318117, 1408100748, 10642345790, 80432918689, 607898868394, 4594402941159, 34723747771300, 262436478814437, 1983452417015597, 14990612333683132, 113296622100170154

Offset: 1

R. H. Hardin, Nov 29 2017

nonn

Column 6 of A295918.

			Some solutions for n=5
..1..0..1..0..1..0. .0..0..0..0..0..0. .1..0..0..0..0..1. .0..0..0..0..0..0
..0..0..0..0..0..0. .1..0..1..0..0..0. .0..0..0..0..0..0. .0..0..1..0..1..0
..0..1..0..1..0..0. .0..0..0..0..0..1. .1..1..0..0..0..1. .0..0..0..0..0..0
..0..0..0..0..0..0. .1..0..0..0..0..0. .1..1..0..0..0..0. .0..0..0..0..1..1
..1..0..1..0..1..0. .0..0..1..0..1..0. .0..0..0..1..0..0. .0..0..0..0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 92

Cf. A295918.

Empirical recurrence of order 92 (see link above)

A295917 Number of n X 7 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1s.

Original entry on oeis.org

34, 277, 2919, 30721, 314044, 3261576, 33703065, 348555744, 3605337986, 37285194645, 385624285944, 3988244570918, 41247771387074, 426598922843727, 4412031119622050, 45630745244822573, 471928833647029372, 4880850060681141219, 50479427900333015968, 522075580210608201142

Offset: 1

R. H. Hardin, Nov 29 2017

nonn

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

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

Column 7 of A295918.

A295912 Number of n X n 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1's.

Original entry on oeis.org

2, 6, 39, 467, 10290, 431844, 33703065, 4933593439, 1353357158724, 695062929397500, 668849535352606829, 1205528922118577365911

Offset: 1

R. H. Hardin, Nov 29 2017

nonn

Diagonal of A295918.

			Some solutions for n=5
..0..0..0..0..0. .1..0..0..0..0. .1..0..1..0..1. .0..0..0..0..0
..0..1..0..0..0. .0..0..1..0..1. .0..0..0..0..0. .0..0..1..0..0
..0..0..0..0..1. .0..0..0..0..0. .0..0..0..0..0. .1..0..0..0..1
..0..0..0..0..0. .0..0..0..0..0. .0..0..0..1..1. .0..0..0..0..0
..1..0..0..0..1. .0..0..1..0..0. .0..1..0..1..1. .0..0..0..0..0

Cf. A295918.

cp's OEIS Frontend

A295913 Number of n X 3 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1's.

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A295914 Number of n X 4 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1s.

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A295915 Number of nX5 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1s.

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A295916 Number of nX6 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1s.

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A295917 Number of n X 7 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1s.

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A295912 Number of n X n 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1's.

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