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A300811
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 8, 4, 8, 29, 29, 8, 16, 108, 170, 108, 16, 32, 401, 1004, 1004, 401, 32, 64, 1490, 5908, 9504, 5908, 1490, 64, 128, 5536, 34836, 90980, 90980, 34836, 5536, 128, 256, 20569, 205369, 872495, 1415898, 872495, 205369, 20569, 256, 512, 76424, 1210811
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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
...2.....8......29.......108.........401..........1490............5536
...4....29.....170......1004........5908.........34836..........205369
...8...108....1004......9504.......90980........872495.........8363710
..16...401....5908.....90980.....1415898......22066384.......343667594
..32..1490...34836....872495....22066384.....559634028.....14189038853
..64..5536..205369...8363710...343667594...14189038853....585611214958
.128.20569.1210811..80174942..5352803078..359766695966..24166702223161
.256.76424.7138574.768542846.83370618870.9121562946307.997271941003944
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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) = 3*a(n-1) +3*a(n-2) -a(n-3) -a(n-4)
k=3: [order 13]
k=4: [order 40]
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..1. .0..0..1..0. .0..1..1..1. .0..0..0..0. .0..0..0..0
..0..1..0..0. .0..1..1..0. .0..0..0..1. .0..1..1..1. .1..1..1..1
..0..1..1..1. .0..1..0..1. .0..1..1..1. .0..0..0..0. .0..0..1..0
..0..0..1..1. .1..0..1..0. .1..1..1..0. .1..1..0..1. .0..0..0..1
..0..1..1..0. .0..0..1..0. .0..1..1..0. .0..0..1..0. .1..1..0..0
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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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