A297993 revision #3
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A297993
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero.
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7
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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, 424, 466, 424, 573, 8, 13, 1933, 1274, 1446, 1446, 1274, 1933, 13, 21, 6538, 3820, 4648, 5100, 4648, 3820, 6538, 21, 34, 22165, 11529, 14888, 18189, 18189, 14888, 11529, 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....424....1274.....3820.....11529......34783.....104826
..2....49...146....466...1446....4648....14888.....47399.....150849.....480015
..3...166...424...1446...5100...18189....62390....213997.....735000....2520806
..5...573..1274...4648..18189...74675...290466...1134198....4475863...17501388
..8..1933..3820..14888..62390..290466..1276012...5745438...26249179..117931466
.13..6538.11529..47399.213997.1134198..5745438..30240388..163303980..862771193
.21.22165.34783.150849.735000.4475863.26249179.163303980.1056360518.6667346762
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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 11] for n>13
k=4: [order 24] for n>27
k=5: [order 99] for n>104
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EXAMPLE
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Some solutions for n=6 k=4
..0..1..1..0. .0..0..0..0. .0..1..0..1. .0..0..0..1. .0..1..1..1
..1..0..1..0. .0..1..1..0. .0..1..0..1. .1..1..1..0. .0..0..0..0
..1..0..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..1. .1..1..1..0
..1..0..1..0. .1..1..1..1. .0..1..0..1. .1..1..1..0. .0..0..1..1
..1..0..1..0. .0..1..1..0. .1..1..0..1. .1..0..0..1. .1..0..0..0
..0..1..0..0. .0..1..1..0. .1..0..0..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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editing
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