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A281936
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T(n,k)=Number of nXk 0..1 arrays with no element equal to more than four of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
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7
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0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 6, 20, 6, 0, 0, 33, 312, 312, 33, 0, 0, 166, 3573, 6304, 3573, 166, 0, 0, 792, 31410, 105766, 105766, 31410, 792, 0, 0, 3654, 252630, 1488168, 2714834, 1488168, 252630, 3654, 0, 0, 16455, 1925590, 19173138, 60084175
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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........1...........6............33..............166................792
.0.....1.......20.........312..........3573............31410.............252630
.0.....6......312........6304........105766..........1488168...........19173138
.0....33.....3573......105766.......2714834.........60084175.........1216849775
.0...166....31410.....1488168......60084175.......2098456730........66997966477
.0...792...252630....19173138....1216849775......66997966477......3373640120486
.0..3654..1925590...233189094...23300375254....2020027689730....160302681247552
.0.16455.14065552..2717934337..428250392864...58434162686355...7305243645203574
.0.72774.99735307.30694746766.7629943002132.1637903530180186.322502538593946476
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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) = 6*a(n-1) -3*a(n-2) -14*a(n-3) -21*a(n-4) -12*a(n-5) -4*a(n-6)
k=3: [order 21] for n>26
k=4: [order 69] for n>74
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..1. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..1..0
..1..1..1..1. .1..1..0..1. .1..1..1..0. .1..0..0..0. .0..1..0..1
..0..1..0..1. .0..1..1..1. .1..1..1..0. .0..1..1..0. .1..0..0..1
..1..1..1..0. .1..1..0..1. .1..0..1..0. .0..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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