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A317036
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 30, 28, 16, 32, 94, 82, 82, 94, 32, 64, 284, 280, 354, 280, 284, 64, 128, 752, 842, 1718, 1718, 842, 752, 128, 256, 2244, 2591, 7523, 11368, 7523, 2591, 2244, 256, 512, 6532, 8141, 33798, 66728, 66728, 33798, 8141, 6532, 512
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OFFSET
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1,2
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COMMENTS
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Table starts
...1....2.....4......8.......16........32..........64..........128
...2....4....14.....28.......94.......284.........752.........2244
...4...14....30.....82......280.......842........2591.........8141
...8...28....82....354.....1718......7523.......33798.......153703
..16...94...280...1718....11368.....66728......417156......2714271
..32..284...842...7523....66728....559097.....4939166.....46085330
..64..752..2591..33798...417156...4939166....64983838....900623946
.128.2244..8141.153703..2714271..46085330...900623946..19235095363
.256.6532.25387.700615.17610616.435634601.12923660734.426907974013
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6
k=3: [order 15] for n>17
k=4: [order 65] for n>67
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..0. .0..0..1..0. .0..0..1..1. .0..0..1..1. .0..0..1..1
..0..0..0..0. .1..0..0..1. .1..1..1..0. .0..0..0..0. .0..0..1..1
..1..0..0..0. .0..0..0..0. .1..1..1..1. .0..0..0..0. .1..1..1..1
..0..0..0..0. .0..0..0..1. .0..1..1..1. .0..0..0..1. .1..1..1..1
..0..0..1..1. .0..1..0..0. .1..1..0..0. .0..1..0..0. .1..0..1..1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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