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A300259
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
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5
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1, 2, 2, 4, 8, 4, 8, 31, 31, 8, 16, 121, 179, 121, 16, 32, 472, 1080, 1080, 472, 32, 64, 1841, 6585, 10363, 6585, 1841, 64, 128, 7181, 40023, 100823, 100823, 40023, 7181, 128, 256, 28010, 243312, 974646, 1588195, 974646, 243312, 28010, 256, 512, 109255, 1479656
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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......31.......121.........472..........1841.............7181
...4.....31.....179......1080........6585.........40023...........243312
...8....121....1080.....10363......100823........974646..........9424684
..16....472....6585....100823.....1588195......24735890........385299869
..32...1841...40023....974646....24735890.....618957455......15475106013
..64...7181..243312...9424684...385299869...15475106013.....620657860617
.128..28010.1479656..91234133..6015414147..388173584774...24999315059414
.256.109255.8997567.882982660.93883095950.9733989458695.1006615871837972
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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) +2*a(n-3)
k=3: [order 11] for n>12
k=4: [order 38] for n>39
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..1. .0..0..1..0. .0..0..1..0. .0..1..0..1. .0..1..1..0
..0..1..0..0. .0..0..1..1. .1..1..1..1. .1..1..1..0. .0..0..1..0
..1..1..0..1. .1..0..1..1. .1..0..0..1. .1..0..0..0. .1..0..1..1
..0..0..0..1. .1..0..0..1. .1..0..0..0. .1..0..1..1. .0..1..1..0
..1..1..0..1. .0..0..1..1. .1..0..1..0. .1..1..0..1. .0..0..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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