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A303242
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
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12
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1, 1, 2, 1, 2, 4, 1, 11, 2, 8, 1, 13, 18, 3, 16, 1, 34, 8, 55, 6, 32, 1, 65, 60, 10, 181, 10, 64, 1, 123, 56, 255, 61, 494, 21, 128, 1, 266, 236, 149, 1106, 160, 1465, 42, 256, 1, 499, 428, 1676, 1373, 5158, 458, 4415, 86, 512, 1, 1037, 1248, 3307, 11111, 7823, 23995, 1748
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OFFSET
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1,3
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COMMENTS
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Table starts
...1..1.....1....1......1.......1........1.........1..........1............1
...2..2....11...13.....34......65......123.......266........499.........1037
...4..2....18....8.....60......56......236.......428.......1248.........3264
...8..3....55...10....255.....149.....1676......3307......18505........65498
..16..6...181...61...1106....1373....11111.....38480.....221943......1162591
..32.10...494..160...5158....7823....90728....421983....3251872.....23282610
..64.21..1465..458..23995...41878...686376...4288552...44547581....435326091
.128.42..4415.1748.108726..277018..5320294..48315454..648070597...8762716079
.256.86.12934.6056.506416.1721671.42575026.536745912.9508520220.176408218876
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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) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 13]
k=4: [order 71] for n>72
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
n=3: [order 20]
n=4: [order 67] for n>68
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..0..0..1. .0..1..1..1. .0..1..1..1. .0..0..1..1
..0..0..1..1. .1..0..0..0. .1..1..1..0. .0..1..1..0. .0..0..1..1
..0..0..1..0. .1..0..1..0. .1..1..1..1. .0..1..1..1. .0..1..1..0
..0..0..1..1. .1..0..0..0. .1..1..1..1. .0..1..1..1. .0..0..1..1
..0..0..1..1. .0..0..0..1. .0..1..1..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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