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A281165
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T(n,k)=Number of nXk 0..1 arrays with no element equal to more than three 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, 5, 5, 0, 0, 18, 40, 18, 0, 0, 85, 477, 477, 85, 0, 0, 346, 3237, 4744, 3237, 346, 0, 0, 1388, 17806, 27229, 27229, 17806, 1388, 0, 0, 5454, 84443, 136138, 163762, 136138, 84443, 5454, 0, 0, 21171, 363824, 619502, 865821, 865821, 619502, 363824
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OFFSET
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1,8
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COMMENTS
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Table starts
.0.....0.......0........0.........0..........0..........0...........0
.0.....0.......5.......18........85........346.......1388........5454
.0.....5......40......477......3237......17806......84443......363824
.0....18.....477.....4744.....27229.....136138.....619502.....2648442
.0....85....3237....27229....163762.....865821....4098895....18213313
.0...346...17806...136138....865821....4716420...22796763...102696802
.0..1388...84443...619502...4098895...22796763..111826676...511077328
.0..5454..363824..2648442..18213313..102696802..511077328..2367603544
.0.21171.1461206.10801150..76987169..438513869.2213577238.10381031459
.0.81250.5575913.42551822.312665502.1799338352.9219387478.43770186654
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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: [order 15]
k=3: [order 27] for n>32
k=4: [order 54] for n>61
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..0..0. .0..1..0..0. .0..1..0..0. .0..1..0..1. .0..1..1..0
..0..0..0..1. .1..1..0..1. .0..0..1..0. .0..0..0..0. .1..1..0..0
..1..1..1..0. .1..0..0..1. .0..1..0..1. .0..1..1..1. .0..1..0..1
..0..1..0..0. .1..1..1..1. .1..0..0..0. .1..1..0..1. .1..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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