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A299249
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5, 6 or 7 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, 6, 18, 1, 1, 31, 18, 18, 31, 1, 1, 65, 30, 55, 30, 65, 1, 1, 130, 87, 192, 192, 87, 130, 1, 1, 253, 202, 652, 1095, 652, 202, 253, 1, 1, 519, 526, 2002, 5042, 5042, 2002, 526, 519, 1, 1, 1018, 1449, 6741, 21251, 35320, 21251, 6741, 1449
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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....6....18.....30.......87.......202........526.........1449
.1..18...18....55....192......652......2002.......6741........23631
.1..31...30...192...1095.....5042.....21251.....111818.......577544
.1..65...87...652...5042....35320....223750....1634125.....12440063
.1.130..202..2002..21251...223750...2044405...21212789....227105938
.1.253..526..6741.111818..1634125..21212789..321811361...4948662848
.1.519.1449.23631.577544.12440063.227105938.4948662848.111378069579
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..197
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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 72] for n>73
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..1. .0..1..0..1
..0..1..0..1. .0..0..0..1. .0..0..0..0. .1..0..1..0. .1..1..1..1
..1..1..0..0. .0..1..1..1. .1..1..0..0. .1..1..1..1. .0..1..1..0
..0..0..1..1. .1..0..0..0. .1..1..0..0. .0..1..1..0. .1..1..0..0
..1..0..1..0. .1..1..0..1. .1..1..0..0. .1..1..0..0. .0..1..1..0
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CROSSREFS
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Column 2 is A297937.
Sequence in context: A298727 A299561 A298382 * A299458 A300096 A294296
Adjacent sequences: A299246 A299247 A299248 * A299250 A299251 A299252
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Feb 05 2018
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STATUS
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approved
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