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A296115
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T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 3 or 4 king-move neighboring 1s.
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8
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 8, 9, 9, 8, 1, 1, 17, 26, 16, 26, 17, 1, 1, 31, 74, 64, 64, 74, 31, 1, 1, 71, 163, 185, 503, 185, 163, 71, 1, 1, 166, 535, 528, 2800, 2800, 528, 535, 166, 1, 1, 365, 1735, 2109, 14057, 29003, 14057, 2109, 1735, 365, 1, 1, 856, 4960
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OFFSET
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1,5
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COMMENTS
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Table starts
.1...1....1....1......1........1.........1...........1.............1
.1...2....3....4......8.......17........31..........71...........166
.1...3....6....9.....26.......74.......163.........535..........1735
.1...4....9...16.....64......185.......528........2109..........7336
.1...8...26...64....503.....2800.....14057......106920........726414
.1..17...74..185...2800....29003....197661.....2401049......28504534
.1..31..163..528..14057...197661...1993970....34228975.....553395326
.1..71..535.2109.106920..2401049..34228975..1061506422...28707285600
.1.166.1735.7336.726414.28504534.553395326.28707285600.1365762093736
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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) = a(n-1) +2*a(n-2) +5*a(n-3) -2*a(n-4) -6*a(n-5) -4*a(n-6)
k=3: [order 11]
k=4: [order 27]
k=5: [order 89]
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EXAMPLE
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Some solutions for n=6 k=4
..0..1..1..0. .0..1..1..0. .0..1..0..0. .0..0..0..0. .0..0..1..0
..0..1..1..0. .0..1..1..0. .1..1..1..0. .0..1..1..0. .0..1..1..1
..0..0..0..0. .0..0..0..0. .0..1..0..0. .0..1..1..0. .0..0..1..0
..1..1..0..0. .0..1..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..1
..1..1..0..0. .1..1..1..0. .0..0..1..1. .0..1..1..0. .0..0..1..1
..0..0..0..0. .0..1..0..0. .0..0..0..0. .0..1..1..0. .0..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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