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A305040
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 6 or 7 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 4, 4, 8, 3, 3, 8, 16, 5, 7, 5, 16, 32, 8, 7, 7, 8, 32, 64, 13, 13, 19, 13, 13, 64, 128, 21, 23, 26, 26, 23, 21, 128, 256, 34, 37, 61, 43, 61, 37, 34, 256, 512, 55, 63, 143, 109, 109, 143, 63, 55, 512, 1024, 89, 109, 277, 319, 362, 319, 277, 109, 89, 1024, 2048, 144
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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......1024.......2048
...2..4...3...5....8...13.....21.....34......55.......89.......144........233
...4..3...7...7...13...23.....37.....63.....109......183.......309........527
...8..5...7..19...26...61....143....277.....568.....1244......2600.......5369
..16..8..13..26...43..109....319....718....1632.....4351.....10773......25199
..32.13..23..61..109..362...1359...3503....9721....31745.....92958.....264320
..64.21..37.143..319.1359...7757..28535..104561...483316...2036051....7957330
.128.34..63.277..718.3503..28535.135992..601711..3666530..20376186..100132274
.256.55.109.568.1632.9721.104561.601711.3230419.25079880.172103176.1036410400
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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) = a(n-1) +a(n-2) for n>4
k=3: a(n) = a(n-1) +2*a(n-3) for n>6
k=4: a(n) = a(n-1) +5*a(n-3) +a(n-4) -4*a(n-6) -4*a(n-7) for n>11
k=5: a(n) = a(n-1) +9*a(n-3) +2*a(n-4) -14*a(n-6) -4*a(n-7) for n>11
k=6: [order 13] for n>19
k=7: [order 46] for n>51
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1
..0..0..0..0. .0..1..0..0. .0..0..1..0. .0..0..0..0. .0..0..1..0
..0..1..1..0. .0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..1..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..0
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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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