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A300314
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 73, 45, 45, 73, 32, 64, 157, 148, 211, 148, 157, 64, 128, 353, 529, 1537, 1537, 529, 353, 128, 256, 869, 1747, 8135, 15171, 8135, 1747, 869, 256, 512, 1993, 5797, 41485, 120072, 120072, 41485, 5797, 1993, 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....7....13......29.......73........157..........353............869
...4...13....20......45......148........529.........1747...........5797
...8...29....45.....211.....1537.......8135........41485.........237494
..16...73...148....1537....15171.....120072......1008622........9188573
..32..157...529....8135...120072....1676663.....23451403......352887797
..64..353..1747...41485..1008622...23451403....543024998....13524308534
.128..869..5797..237494..9188573..352887797..13524308534...558233828840
.256.1993.19584.1335377.81099064.5253872974.332995274077.22733280314275
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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) = 4*a(n-1) -5*a(n-2) +10*a(n-3) -24*a(n-4) +16*a(n-5) for n>6
k=3: [order 16] for n>17
k=4: [order 55] for n>59
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..0. .0..0..0..1. .0..1..0..1. .0..1..0..0. .0..0..1..0
..1..1..0..1. .1..0..0..0. .1..1..0..0. .1..1..0..1. .1..1..1..0
..0..0..0..0. .1..1..0..0. .1..1..1..1. .1..1..1..1. .0..1..1..1
..1..0..0..0. .1..1..0..0. .1..0..1..0. .1..1..1..1. .0..1..1..1
..0..1..1..0. .0..1..0..1. .0..0..1..0. .0..1..1..0. .1..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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