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A301951
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 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, 5, 5, 0, 3, 16, 20, 13, 0, 5, 52, 123, 83, 34, 0, 8, 169, 680, 947, 342, 89, 0, 13, 549, 4070, 9084, 7326, 1411, 233, 0, 21, 1784, 23565, 98839, 120815, 56710, 5820, 610, 0, 34, 5797, 138014, 1029960, 2406169, 1608681, 439078, 24007, 1597, 0
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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
.0....2.....5.......16.........52..........169.............549
.0....5....20......123........680.........4070...........23565
.0...13....83......947.......9084........98839.........1029960
.0...34...342.....7326.....120815......2406169........45013365
.0...89..1411....56710....1608681.....58609226......1969215107
.0..233..5820...439078...21418808...1427656268.....86143630040
.0..610.24007..3399722..285190208..34776685046...3768464135104
.0.1597.99026.26323903.3797277789.847137052736.164856325277648
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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)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 4*a(n-1) +a(n-2) -2*a(n-3)
k=4: a(n) = 9*a(n-1) -8*a(n-2) -14*a(n-3) +4*a(n-4) +4*a(n-5) -a(n-6)
k=5: [order 13] for n>15
k=6: [order 26] for n>28
k=7: [order 43] for n>47
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6
n=3: [order 10] for n>12
n=4: [order 36] for n>40
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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..0..1. .0..0..1..1
..0..1..1..0. .0..1..1..0. .0..1..1..1. .0..0..1..1. .0..1..0..1
..0..0..0..0. .1..1..0..0. .0..0..1..1. .0..0..1..0. .0..0..1..0
..1..1..1..1. .1..0..0..1. .1..1..1..1. .0..0..0..0. .1..1..0..0
..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..1..1..1. .1..1..1..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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