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A300096
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
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7
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1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 18, 7, 18, 1, 1, 31, 19, 19, 31, 1, 1, 65, 35, 56, 35, 65, 1, 1, 130, 95, 203, 203, 95, 130, 1, 1, 253, 225, 672, 1301, 672, 225, 253, 1, 1, 519, 575, 2168, 5953, 5953, 2168, 575, 519, 1, 1, 1018, 1563, 7287, 27614, 43848, 27614, 7287, 1563
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OFFSET
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1,5
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COMMENTS
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Table starts
.1...1....1.....1......1........1.........1...........1............1
.1...5....7....18.....31.......65.......130.........253..........519
.1...7....7....19.....35.......95.......225.........575.........1563
.1..18...19....56....203......672......2168........7287........25652
.1..31...35...203...1301.....5953.....27614......144519.......776608
.1..65...95...672...5953....43848....310762.....2373454.....19198301
.1.130..225..2168..27614...310762...3273425....36840985....436133886
.1.253..575..7287.144519..2373454..36840985...616964357..10746198229
.1.519.1563.25652.776608.19198301.436133886.10746198229.279529477217
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..180
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
k=3: [order 19] for n>20
k=4: [order 71] for n>72
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..0. .0..0..1..1. .0..0..1..0. .0..0..0..0. .0..0..1..0
..0..1..1..1. .0..0..1..1. .1..0..1..1. .0..1..1..0. .1..0..0..0
..1..0..0..0. .0..0..1..1. .1..1..0..0. .1..0..1..0. .1..1..1..0
..1..1..1..0. .0..0..0..0. .0..0..0..0. .1..0..1..0. .0..0..0..1
..1..0..1..1. .0..0..0..0. .0..0..0..0. .1..1..0..0. .1..0..1..1
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CROSSREFS
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Column 2 is A297937.
Sequence in context: A298382 A299249 A299458 * A294296 A078181 A054110
Adjacent sequences: A300093 A300094 A300095 * A300097 A300098 A300099
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Feb 24 2018
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STATUS
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approved
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