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A317741
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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8
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0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 4, 3, 3, 4, 0, 0, 9, 2, 4, 2, 9, 0, 0, 22, 4, 14, 14, 4, 22, 0, 0, 53, 6, 23, 14, 23, 6, 53, 0, 0, 130, 14, 35, 38, 38, 35, 14, 130, 0, 0, 320, 14, 98, 74, 22, 74, 98, 14, 320, 0, 0, 788, 22, 213, 149, 36, 36, 149, 213, 22, 788, 0, 0, 1942, 43
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OFFSET
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1,12
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COMMENTS
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Table starts
.0...0..0...0...0...0....0...0....0....0.....0.....0.....0......0......0
.0...1..1...2...4...9...22..53..130..320...788..1942..4787..11801..29093
.0...1..1...3...2...4....6..14...14...22....43....68....82....147....246
.0...2..3...4..14..23...35..98..213..448..1053..2285..5170..11442..25631
.0...4..2..14..14..38...74.149..269..662..1294..2721..5911..12084..25175
.0...9..4..23..38..22...36.140..146..218...736..1072..1890...4505...8860
.0..22..6..35..74..36..274.280.1065.1939..5947.13101.35847..83062.222994
.0..53.14..98.149.140..280.676..914.2388..3845.11110.14133..42876..69411
.0.130.14.213.269.146.1065.914.3242.5466.15470.37531.94202.234901.706951
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) -a(n-6)
k=3: [order 10] for n>13
k=4: [order 23] for n>26
k=5: [order 33] for n>39
k=6: [order 56] for n>63
k=7: [order 97] for n>108
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1. .0..1..1..1
..1..0..0..1. .1..0..0..0. .1..0..0..1. .1..0..0..0. .1..0..0..0
..0..0..1..0. .0..1..1..1. .0..0..1..0. .1..0..1..1. .0..0..1..1
..1..1..1..0. .1..1..1..0. .1..1..1..0. .0..1..1..0. .1..1..1..0
..0..1..0..1. .0..0..0..1. .0..1..0..1. .0..1..0..1. .0..0..0..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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