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A301999
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
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12
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0, 1, 0, 1, 2, 0, 2, 2, 5, 0, 3, 8, 5, 13, 0, 5, 18, 26, 15, 34, 0, 8, 50, 84, 74, 48, 89, 0, 13, 128, 309, 468, 200, 155, 233, 0, 21, 338, 1108, 2036, 2856, 530, 499, 610, 0, 34, 882, 3979, 10982, 14016, 17800, 1394, 1602, 1597, 0, 55, 2312, 14314, 53440, 122232
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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
.0....2....2....8......18.......50........128.........338...........882
.0....5....5...26......84......309.......1108........3979.........14314
.0...13...15...74.....468.....2036......10982.......53440........271596
.0...34...48..200....2856....14016.....122232......813704.......6066698
.0...89..155..530...17800...100176....1366374....12824770.....133115004
.0..233..499.1394..110036...729297...15243860...204666568....2933712940
.0..610.1602.3656..674984..5333386..169636124..3267873712...64653790404
.0.1597.5137.9578.4130664.39000114.1884309898.52110883753.1423142192108
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..311
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 5*a(n-1) -7*a(n-2) +4*a(n-3)
k=4: a(n) = 4*a(n-1) -4*a(n-2) +a(n-3)
k=5: [order 11] for n>12
k=6: [order 32] for n>33
k=7: [order 52] for n>54
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)
n=3: [order 20]
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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..1..1. .0..0..1..1. .0..0..1..0
..1..1..0..1. .1..1..0..0. .0..0..0..0. .0..1..0..0. .0..1..0..0
..1..0..1..0. .1..1..0..1. .1..1..1..1. .1..0..1..0. .1..1..0..0
..0..1..0..1. .1..0..1..0. .0..0..1..0. .0..1..0..1. .1..1..1..1
..0..0..1..1. .1..1..0..0. .0..1..0..0. .1..0..1..1. .0..0..1..1
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CROSSREFS
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Column 2 is A001519.
Row 1 is A000045(n-1).
Row 2 is A175395(n-1).
Sequence in context: A118658 A165912 A301823 * A171936 A071055 A183034
Adjacent sequences: A301996 A301997 A301998 * A302000 A302001 A302002
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Mar 30 2018
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STATUS
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approved
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