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A297943
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 5 king-move adjacent elements, with upper left element zero.
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8
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1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 18, 4, 18, 1, 1, 31, 14, 14, 31, 1, 1, 65, 16, 33, 16, 65, 1, 1, 130, 51, 74, 74, 51, 130, 1, 1, 253, 102, 226, 330, 226, 102, 253, 1, 1, 519, 258, 694, 1032, 1032, 694, 258, 519, 1, 1, 1018, 667, 2121, 3640, 3977, 3640, 2121, 667, 1018, 1
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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..........1
.1...5...7...18....31.....65.....130......253......519......1018.......2055
.1...7...4...14....16.....51.....102......258......667......1716.......4557
.1..18..14...33....74....226.....694.....2121.....6517.....20208......62318
.1..31..16...74...330...1032....3640....12800....44663....159995.....572956
.1..65..51..226..1032...3977...16198....66625...279485...1186383....5055084
.1.130.102..694..3640..16198...76374...376126..1869918...9484034...48011978
.1.253.258.2121.12800..66625..376126..2200020.12989533..78218401..469760261
.1.519.667.6517.44663.279485.1869918.12989533.90659562.647989857.4623257850
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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) +3*a(n-2) -4*a(n-4) for n>5
k=3: [order 16] for n>17
k=4: [order 57] for n>59
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EXAMPLE
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Some solutions for n=7 k=4
..0..0..1..1. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..1..1..0
..0..1..1..0. .1..0..1..0. .1..1..1..0. .0..1..1..0. .1..1..0..0
..1..0..0..0. .1..1..0..0. .1..0..1..0. .0..1..0..1. .0..1..1..1
..0..1..1..1. .1..0..1..0. .1..0..0..0. .0..1..0..1. .1..1..0..1
..0..0..1..0. .0..1..0..1. .1..1..1..0. .0..0..1..1. .1..0..1..0
..1..0..1..1. .0..1..0..1. .0..0..0..1. .1..1..1..0. .1..0..0..1
..0..0..0..1. .0..0..1..1. .1..0..1..1. .1..0..1..1. .1..1..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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