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A295352
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T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 3 1s.
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8
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2, 3, 3, 5, 8, 5, 8, 20, 20, 8, 13, 51, 76, 51, 13, 21, 132, 299, 299, 132, 21, 34, 341, 1198, 1877, 1198, 341, 34, 55, 883, 4775, 11964, 11964, 4775, 883, 55, 89, 2293, 19214, 76688, 123783, 76688, 19214, 2293, 89, 144, 5964, 77650, 499257, 1290706, 1290706
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OFFSET
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1,1
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COMMENTS
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Table starts
..2....3......5........8.........13...........21.............34..............55
..3....8.....20.......51........132..........341............883............2293
..5...20.....76......299.......1198.........4775..........19214...........77650
..8...51....299.....1877......11964........76688.........499257.........3279206
.13..132...1198....11964.....123783......1290706.......13795489.......149583916
.21..341...4775....76688....1290706.....22091007......390440690......7029925681
.34..883..19214...499257...13795489....390440690....11500075769....345835713946
.55.2293..77650..3279206..149583916...7029925681...345835713946..17390584281932
.89.5964.314916.21697056.1639232052.128195710958.10540491064074.885995909117214
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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) = 4*a(n-1) -3*a(n-2) -4*a(n-4) -a(n-5) +a(n-6)
k=3: [order 18]
k=4: [order 45]
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EXAMPLE
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Some solutions for n=5 k=4
..1..0..1..0. .1..0..1..0. .1..0..0..0. .0..1..0..0. .0..1..1..1
..0..0..0..1. .0..0..0..1. .0..0..1..0. .1..0..0..0. .0..1..0..1
..0..1..0..0. .0..1..0..0. .1..0..0..0. .0..0..0..1. .0..1..0..1
..1..0..0..0. .1..0..0..0. .0..0..1..0. .0..1..0..0. .0..1..1..1
..0..0..0..1. .0..0..1..0. .0..1..0..1. .1..0..0..0. .0..0..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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