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A301964
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
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12
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1, 2, 2, 3, 5, 4, 5, 6, 13, 8, 8, 9, 16, 34, 16, 13, 14, 25, 40, 89, 32, 21, 22, 41, 64, 100, 233, 64, 34, 35, 74, 111, 169, 252, 610, 128, 55, 56, 132, 219, 311, 441, 632, 1597, 256, 89, 90, 239, 443, 749, 874, 1156, 1588, 4181, 512, 144, 145, 437, 904, 1803, 2544, 2454
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OFFSET
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1,2
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COMMENTS
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Table starts
...1....2....3....5.....8.....13.....21......34.......55........89.......144
...2....5....6....9....14.....22.....35......56.......90.......145.......234
...4...13...16...25....41.....74....132.....239......437.......800......1468
...8...34...40...64...111....219....443.....904.....1860......3856......8015
..16...89..100..169...311....749...1803....4257....10353.....25491.....62623
..32..233..252..441...874...2544...7795...22456....66659....203926....621905
..64..610..632.1156..2454...8705..33860..120603...444357...1715911...6574776
.128.1597.1588.3025..6906..29750.148299..655332..3014296..14863160..72345489
.256.4181.3988.7921.19427.101869.646838.3557239.20467528.129324707.802690313
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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)
k=3: a(n) = a(n-1) +3*a(n-2) +2*a(n-3)
k=4: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3) for n>4
k=5: a(n) = 2*a(n-1) +3*a(n-2) -a(n-3) -2*a(n-4) -3*a(n-5) +2*a(n-6) for n>8
k=6: [order 11] for n>12
k=7: [order 14] for n>17
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-3) for n>5
n=3: a(n) = 2*a(n-1) -a(n-4) for n>6
n=4: a(n) = 2*a(n-1) +a(n-3) -a(n-4) -2*a(n-6) +a(n-7) for n>9
n=5: [order 14] for n>17
n=6: [order 27] for n>32
n=7: [order 47] for n>52
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..0. .0..0..1..0
..0..1..0..1. .0..0..0..1. .0..1..0..1. .0..0..1..0. .1..1..1..0
..0..0..0..1. .0..1..0..1. .0..1..0..1. .1..0..1..1. .1..0..1..0
..0..1..1..1. .0..1..1..1. .1..0..1..0. .1..0..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .1..0..1..1. .1..1..0..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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