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A297823
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 king-move adjacent elements, with upper left element zero.
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8
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0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 49, 48, 49, 3, 5, 166, 146, 146, 166, 5, 8, 573, 399, 466, 399, 573, 8, 13, 1933, 1114, 1395, 1395, 1114, 1933, 13, 21, 6538, 3124, 4306, 4444, 4306, 3124, 6538, 21, 34, 22165, 8861, 13417, 14237, 14237, 13417, 8861, 22165, 34
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OFFSET
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1,5
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COMMENTS
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Table starts
..0.....1.....1......2......3.......5.......8.......13.......21........34
..1.....4....17.....49....166.....573....1933.....6538....22165.....75089
..1....17....48....146....399....1114....3124.....8861....25130.....71196
..2....49...146....466...1395....4306...13417....41512...128084....395130
..3...166...399...1395...4444...14237...43931...134395...412427...1268252
..5...573..1114...4306..14237...46701..146530...456814..1433279...4501076
..8..1933..3124..13417..43931..146530..467104..1485611..4742326..15121792
.13..6538..8861..41512.134395..456814.1485611..4833331.15742632..51146914
.21.22165.25130.128084.412427.1433279.4742326.15742632.52153064.172452330
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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) +a(n-2)
k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
k=3: [order 9] for n>11
k=4: [order 18] for n>21
k=5: [order 49] for n>55
k=6: [order 98] for n>107
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EXAMPLE
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Some solutions for n=6 k=4
..0..0..1..1. .0..0..1..1. .0..0..1..0. .0..0..0..0. .0..1..1..0
..1..0..0..1. .0..1..0..0. .0..1..0..0. .0..1..1..0. .1..0..0..1
..1..1..1..0. .1..1..0..1. .0..1..1..1. .1..0..0..1. .1..1..0..1
..0..0..0..1. .0..1..0..1. .1..0..0..0. .0..1..1..0. .0..1..0..1
..1..1..0..1. .0..1..0..1. .1..1..1..1. .1..0..0..1. .1..0..0..1
..1..1..0..1. .0..0..1..0. .0..0..0..1. .0..1..1..0. .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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