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A317823
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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8
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0, 1, 1, 1, 5, 1, 2, 16, 16, 2, 3, 50, 35, 50, 3, 5, 160, 135, 135, 160, 5, 8, 511, 356, 702, 356, 511, 8, 13, 1634, 1113, 2726, 2726, 1113, 1634, 13, 21, 5226, 3150, 11768, 8556, 11768, 3150, 5226, 21, 34, 16716, 9484, 48526, 47374, 47374, 48526, 9484, 16716, 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
..1.....5....16.....50.....160......511......1634.......5226.......16716
..1....16....35....135.....356.....1113......3150.......9484.......27522
..2....50...135....702....2726....11768.....48526.....203049......846901
..3...160...356...2726....8556....47374....179111.....878802.....3604079
..5...511..1113..11768...47374...296968...1458418....8231398....43470698
..8..1634..3150..48526..179111..1458418...7370716...49813114...285365386
.13..5226..9484.203049..878802..8231398..49813114..384248160..2679172247
.21.16716.27522.846901.3604079.43470698.285365386.2679172247.21424520640
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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) -3*a(n-4) -2*a(n-5) -a(n-6)
k=3: [order 16] for n>18
k=4: [order 37] for n>43
k=5: [order 94] for n>99
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..0. .0..0..1..1. .0..1..1..0. .0..0..1..0. .0..1..1..0
..0..1..1..0. .1..1..1..0. .1..0..0..1. .1..1..1..1. .0..1..1..1
..1..1..1..0. .0..1..1..0. .0..0..0..1. .1..1..1..0. .0..1..1..0
..0..1..1..0. .0..1..0..1. .1..0..1..1. .0..1..1..0. .0..1..1..0
..0..1..0..1. .1..0..0..1. .1..0..1..0. .0..1..1..0. .0..1..1..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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