A186168 -id:A186168 - cp's OEIS frontend

A186161 1/4 the number of n X 2 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

1, 7, 48, 321, 2175, 14748, 99933, 677283, 4590168, 31108893, 210834267, 1428886932, 9683993481, 65631317487, 444803049600, 3014563174089, 20430595384935, 138464249604684, 938413592805957, 6359909317239723

Offset: 1

R. H. Hardin, Feb 13 2011

nonn

Column 2 of A186168.

			Some solutions for 4 X 2 with a(1,1)=0:
..0..0....0..1....0..0....0..0....0..3....0..2....0..0....0..2....0..2....0..0
..2..2....0..1....2..3....1..1....0..3....0..2....0..2....0..2....0..2....0..0
..0..2....3..3....2..3....3..3....2..0....0..2....3..2....3..3....1..1....2..2
..0..0....0..0....1..1....3..3....2..0....0..2....3..3....3..3....1..1....0..0

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A186168.

Empirical: a(n) = 5*a(n-1) + 11*a(n-2) + 9*a(n-3) - 9*a(n-4) - 27*a(n-5).

Empirical g.f.: x*(1 + 2*x + 2*x^2 - 5*x^3 - 12*x^4) / (1 - 5*x - 11*x^2 - 9*x^3 + 9*x^4 + 27*x^5). - Colin Barker, Apr 17 2018

A186162 1/4 the number of nX3 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

1, 48, 702, 14364, 253341, 4762206, 87054174, 1610684397, 29645381115, 546876640548, 10078456022415, 185816448936792, 3425262221153151, 63144918326035629, 1164039832228952691, 21458721711659114403

Offset: 1

R. H. Hardin Feb 13 2011

nonn

Column 3 of A186168

			Some solutions for 4X3 with a(1,1)=0
..0..0..0....0..1..0....0..0..0....0..2..2....0..2..2....0..3..3....0..0..3
..0..3..3....0..1..0....2..2..0....0..2..3....0..3..1....0..2..2....0..1..3
..3..1..1....3..1..3....3..2..2....0..3..3....3..3..1....0..1..3....2..1..1
..3..2..2....3..1..3....3..3..3....1..1..1....1..1..1....1..1..3....2..0..0

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n)=12*a(n-1)+138*a(n-2)-297*a(n-3)-1095*a(n-4)-588*a(n-5)+4871*a(n-6)+10632*a(n-7)-24375*a(n-8)+40893*a(n-9)-59724*a(n-10)-68247*a(n-11)-358891*a(n-12)+1270395*a(n-13)+391440*a(n-14)-2188134*a(n-15)+133083*a(n-16)+1270323*a(n-17)+3453273*a(n-18)+1073817*a(n-19)-5417199*a(n-20)-4448358*a(n-21)-13463172*a(n-22)-12754584*a(n-23)

A186163 1/4 the number of nX4 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

4, 321, 14364, 751266, 37402872, 1899336597, 95752776009, 4840082975532, 244420512852030, 12347377339339755, 623671780419814416, 31503432697236966789, 1591300459563274835532, 80380228276030331585859

Offset: 1

R. H. Hardin Feb 13 2011

nonn

Column 4 of A186168

			Some solutions for 6X4 with a(1,1)=0
..0..0..0..1....0..0..2..2....0..0..0..3....0..0..1..1....0..0..3..3
..0..2..2..1....0..2..2..1....0..2..2..3....0..2..2..1....0..2..2..2
..0..0..2..3....0..0..1..1....0..0..3..0....0..0..1..1....0..0..3..1
..2..0..0..3....2..0..2..2....2..0..3..0....2..0..3..3....2..0..3..1
..2..2..0..0....2..3..3..1....2..2..2..0....2..2..2..2....2..0..2..2
..0..0..2..2....0..0..0..1....0..0..1..1....0..0..1..1....2..2..0..0

R. H. Hardin, Table of n, a(n) for n = 1..200

A186164 1/4 the number of nX5 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

7, 2175, 253341, 37402872, 5033988714, 704281652979, 96951738076992, 13435825601048421, 1856827788245959473, 256908205340960558187, 35528479510856892673200, 4914300705034627821533085

Offset: 1

R. H. Hardin Feb 13 2011

nonn

Column 5 of A186168

			Some solutions for 4X5 with a(1,1)=0
..0..0..0..1..1....0..0..0..0..0....0..0..0..3..3....0..0..0..2..2
..0..2..0..1..2....0..2..1..1..1....0..2..0..1..3....0..2..0..2..1
..1..2..2..1..2....0..2..2..3..3....0..2..2..1..1....0..2..0..3..1
..1..1..0..0..2....3..3..3..0..0....0..3..3..0..0....0..2..0..3..3

R. H. Hardin, Table of n, a(n) for n = 1..21

A186160 1/4 the number of n X n 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

0, 7, 702, 751266, 5033988714, 268995986029278

Offset: 1

R. H. Hardin Feb 13 2011

nonn

Diagonal of A186168

			Some solutions for 4X4 with a(1,1)=0
..0..2..0..2....0..0..2..0....0..2..1..1....0..0..2..2....0..2..2..1
..0..2..0..2....0..0..2..0....0..2..0..0....0..2..1..2....0..0..0..1
..1..2..3..3....2..3..3..3....2..1..1..0....2..2..1..0....2..3..3..1
..1..1..1..1....2..3..2..2....2..2..1..0....3..3..3..0....2..3..0..0

A186165 1/4 the number of nX6 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

19, 14748, 4762206, 1899336597, 704281652979, 268995986029278, 101554003879403823, 38514280297010210802

Offset: 1

R. H. Hardin Feb 13 2011

nonn

Column 6 of A186168

			Some solutions for 4X6 with a(1,1)=0
..0..0..0..2..2..2....0..0..0..2..2..0....0..0..0..2..2..0....0..0..0..2..2..0
..0..2..0..0..0..2....0..2..0..0..2..0....0..2..0..0..0..0....0..2..0..0..3..0
..3..2..1..2..0..3....3..2..1..1..2..0....0..2..2..2..2..2....1..2..2..3..3..0
..3..1..1..2..0..3....3..0..0..0..2..0....0..0..0..0..1..1....1..0..0..3..2..2

A186166 1/4 the number of n X 7 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

40, 99933, 87054174, 95752776009, 96951738076992, 101554003879403823

Offset: 1

R. H. Hardin Feb 13 2011

nonn

Column 7 of A186168.

			Some solutions for 4 X 7 with a(1,1) = 0
..0..0..2..0..0..0..1....0..0..2..0..0..3..0....0..0..2..0..0..0..0
..0..0..2..0..2..2..1....0..0..2..0..3..3..0....0..0..2..0..2..2..1
..2..2..0..2..3..3..1....2..2..0..2..3..0..1....2..2..0..1..2..1..1
..0..0..0..2..3..2..2....0..0..0..2..0..0..1....0..0..0..1..1..3..3

Cf. A186168.

A186167 1/4 the number of nX8 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

Original entry on oeis.org

97, 677283, 1610684397, 4840082975532, 13435825601048421, 38514280297010210802

Offset: 1

R. H. Hardin Feb 13 2011

nonn

Column 8 of A186168

			Some solutions for 3X8 with a(1,1)=0
..0..0..0..0..2..1..1..0....0..0..0..0..3..0..3..3....0..0..0..0..0..3..3..0
..0..1..1..2..2..3..1..0....0..1..1..0..3..0..0..3....0..1..1..2..2..1..0..0
..0..0..0..0..0..3..3..0....0..0..0..0..3..3..0..0....0..0..0..0..2..1..3..3

cp's OEIS Frontend

A186161 1/4 the number of n X 2 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

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A186162 1/4 the number of nX3 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

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A186163 1/4 the number of nX4 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

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A186164 1/4 the number of nX5 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

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A186160 1/4 the number of n X n 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

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A186165 1/4 the number of nX6 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

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A186166 1/4 the number of n X 7 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

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Examples

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A186167 1/4 the number of nX8 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

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Author

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Examples