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A281344
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T(n,k)=Number of nXk 0..1 arrays with no element equal to more than three 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, 25, 25, 8, 16, 85, 68, 85, 16, 32, 286, 193, 193, 286, 32, 64, 969, 544, 607, 544, 969, 64, 128, 3281, 1539, 1892, 1892, 1539, 3281, 128, 256, 11114, 4355, 5868, 6256, 5868, 4355, 11114, 256, 512, 37649, 12332, 18189, 19700, 19700, 18189
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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......128.......256.......512
...2......8....25.....85.....286.....969.....3281....11114.....37649....127541
...4.....25....68....193.....544....1539.....4355....12332.....34907.....98797
...8.....85...193....607....1892....5868....18189....56154....173062....534110
..16....286...544...1892....6256...19700....60540...185696....569832...1754082
..32....969..1539...5868...19700...63168...198619...620828...1944159...6105081
..64...3281..4355..18189...60540..198619...639142..2039214...6489813..20683647
.128..11114.12332..56154..185696..620828..2039214..6658147..21625033..70229690
.256..37649.34907.173062..569832.1944159..6489813.21625033..71489598.235986575
.512.127541.98797.534110.1754082.6105081.20683647.70229690.235986575.791069059
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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) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5)
k=3: [order 9] for n>10
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=4 k=4
..0..1..0..0. .0..0..1..1. .0..0..0..1. .0..0..0..0. .0..1..1..1
..0..1..0..1. .0..1..0..1. .0..1..1..0. .0..1..1..1. .0..1..0..0
..1..1..0..1. .0..1..0..0. .1..0..0..1. .1..0..0..0. .0..1..0..1
..0..0..0..1. .1..0..1..1. .1..1..1..0. .1..0..1..1. .0..1..0..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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