A295781 -id:A295781 - cp's OEIS frontend

A295776 Number of n X 3 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s.

5, 19, 56, 198, 665, 2213, 7479, 25105, 84326, 283532, 952661, 3201517, 10759441, 36157455, 121511416, 408352614, 1372308917, 4611790689, 15498404475, 52083999509, 175033735054, 588219141252, 1976771852673, 6643148349849

Offset: 1

R. H. Hardin, Nov 27 2017

nonn

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

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

Column 3 of A295781.

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

Empirical g.f.: x*(5 + 9*x + 3*x^2 - x^3 + 2*x^4) / (1 - 2*x - 3*x^2 - 6*x^3 + 3*x^4 - 2*x^5). - Colin Barker, Feb 22 2019

A295777 Number of nX4 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s.

Original entry on oeis.org

8, 49, 198, 1059, 5263, 25529, 127731, 630988, 3118368, 15452696, 76444609, 378316752, 1872559828, 9266918261, 45863407707, 226985095214, 1123365612319, 5559672436516, 27515436853783, 136176807358073, 673954171761877

Offset: 1

R. H. Hardin, Nov 27 2017

nonn

Column 4 of A295781.

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

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

Cf. A295781.

Empirical: a(n) = 4*a(n-1) +6*a(n-2) +6*a(n-3) -58*a(n-4) -20*a(n-5) +29*a(n-6) -92*a(n-7) +7*a(n-8) +2*a(n-9) -2*a(n-10)

A295778 Number of nX5 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s.

Original entry on oeis.org

13, 123, 665, 5263, 37897, 262707, 1905471, 13577504, 96726819, 692170604, 4940333676, 35278772122, 252010713334, 1799646642508, 12852977396156, 91796379668972, 655591261804564, 4682182568641239, 33439719466609663

Offset: 1

R. H. Hardin, Nov 27 2017

nonn

Column 5 of A295781.

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

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

Cf. A295781.

Empirical: a(n) = 8*a(n-1) +2*a(n-2) -10*a(n-3) -408*a(n-4) +303*a(n-5) +1027*a(n-6) +905*a(n-7) +128*a(n-8) -5240*a(n-9) -261*a(n-10) +3150*a(n-11) -1753*a(n-12) +522*a(n-13) +691*a(n-14) +1536*a(n-15) +1326*a(n-16) -327*a(n-17) +802*a(n-18) -212*a(n-19) -739*a(n-20) -14*a(n-21) +4*a(n-22)

A295779 Number of nX6 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s.

Original entry on oeis.org

21, 297, 2213, 25529, 262707, 2602065, 27085621, 276224518, 2819029784, 28899641330, 295437343180, 3022217370837, 30925095105256, 316343570292406, 3236407313791828, 33110664446316449, 338735015559436300

Offset: 1

R. H. Hardin, Nov 27 2017

nonn

Column 6 of A295781.

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

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

Cf. A295781.

Empirical: a(n) = 10*a(n-1) +25*a(n-2) -54*a(n-3) -1950*a(n-4) -771*a(n-5) +17511*a(n-6) +47337*a(n-7) -9028*a(n-8) -267305*a(n-9) -239276*a(n-10) -317469*a(n-11) -96151*a(n-12) +93601*a(n-13) -2823773*a(n-14) +8974347*a(n-15) +15080690*a(n-16) -8251554*a(n-17) +13847286*a(n-18) +53084975*a(n-19) -4187575*a(n-20) -47624792*a(n-21) +61798212*a(n-22) +38117156*a(n-23) -94637807*a(n-24) +18477679*a(n-25) +72789985*a(n-26) -42141667*a(n-27) -29245294*a(n-28) +37728290*a(n-29) -5310570*a(n-30) -21624452*a(n-31) +10924920*a(n-32) +3789229*a(n-33) -6379194*a(n-34) -82479*a(n-35) +1496226*a(n-36) -350920*a(n-37) -274644*a(n-38) +61610*a(n-39) +10150*a(n-40) +3483*a(n-41) -74*a(n-42) +6*a(n-43)

A295780 Number of nX7 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s.

Original entry on oeis.org

34, 739, 7479, 127731, 1905471, 27085621, 409525082, 6037613762, 89072774496, 1321788634101, 19544371605946, 289230460757404, 4281937924123280, 63365816364621759, 937874156712320997, 13881506306783920348

Offset: 1

R. H. Hardin, Nov 27 2017

nonn

Column 7 of A295781.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 91

Cf. A295781.

Empirical recurrence of order 91 (see link above)

A295775 Number of n X n 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1's.

Original entry on oeis.org

2, 9, 56, 1059, 37897, 2602065, 409525082, 128171125105, 83333126432833, 114403160523019326, 323325261181740261922, 1905368274130445991781276

Offset: 1

R. H. Hardin, Nov 27 2017

nonn

Diagonal of A295781.

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

Cf. A295781.

cp's OEIS Frontend

A295776 Number of n X 3 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s.

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A295777 Number of nX4 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s.

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A295778 Number of nX5 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s.

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A295779 Number of nX6 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s.

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A295780 Number of nX7 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s.

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A295775 Number of n X n 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1's.

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