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A281837
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T(n,k)=Number of nXk 0..1 arrays with no element equal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards.
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8
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1, 2, 2, 4, 8, 4, 8, 31, 31, 8, 16, 121, 163, 121, 16, 32, 472, 926, 926, 472, 32, 64, 1841, 5315, 8240, 5315, 1841, 64, 128, 7181, 30387, 74240, 74240, 30387, 7181, 128, 256, 28010, 174121, 663300, 1053407, 663300, 174121, 28010, 256, 512, 109255, 998069
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OFFSET
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1,2
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COMMENTS
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Table starts
...1......2........4..........8...........16.............32................64
...2......8.......31........121..........472...........1841..............7181
...4.....31......163........926.........5315..........30387............174121
...8....121......926.......8240........74240.........663300...........5954670
..16....472.....5315......74240......1053407.......14783996.........208837689
..32...1841....30387.....663300.....14783996......324602161........7184856176
..64...7181...174121....5954670....208837689.....7184856176......249711414322
.128..28010...998069...53530609...2957076233...159608206156.....8720904906157
.256.109255..5720443..481128867..41858516870..3543794795757...304343654274741
.512.426157.32788987.4324987861.592613243866.78695552108964.10622958299884002
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..180
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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) = 3*a(n-1) +3*a(n-2) +2*a(n-3)
k=3: [order 7] for n>8
k=4: [order 23] for n>24
k=5: [order 97] for n>99
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..1. .0..1..1..0. .0..1..1..0. .0..1..0..1. .0..0..0..1
..0..0..0..0. .0..1..0..0. .0..0..1..0. .0..1..0..1. .0..1..0..0
..1..1..1..0. .0..1..0..1. .1..0..1..0. .1..1..0..1. .0..1..1..1
..1..0..0..0. .1..1..0..1. .1..1..1..0. .0..0..0..0. .1..0..1..0
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CROSSREFS
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Column 1 is A000079(n-1).
Sequence in context: A317004 A316822 A317572 * A299081 A299844 A299001
Adjacent sequences: A281834 A281835 A281836 * A281838 A281839 A281840
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Jan 31 2017
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STATUS
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approved
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