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A298589
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
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7
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 9, 2, 1, 1, 5, 5, 5, 5, 1, 1, 9, 16, 4, 16, 9, 1, 1, 22, 31, 13, 13, 31, 22, 1, 1, 45, 28, 31, 65, 31, 28, 45, 1, 1, 101, 87, 83, 233, 233, 83, 87, 101, 1, 1, 218, 125, 262, 441, 1112, 441, 262, 125, 218, 1, 1, 477, 185, 819, 1765, 4620, 4620, 1765
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OFFSET
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1,12
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COMMENTS
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Table starts
.1...1...1...1....1......1.......1........1..........1...........1............1
.1...1...1...2....5......9......22.......45........101.........218..........477
.1...1...9...5...16.....31......28.......87........125.........185..........418
.1...2...5...4...13.....31......83......262........819........2690.........8887
.1...5..16..13...65....233.....441.....1765.......7431.......28212.......121244
.1...9..31..31..233...1112....4620....29589.....169601.....1004366......6170528
.1..22..28..83..441...4620...26343...240692....2382399....22651784....228684042
.1..45..87.262.1765..29589..240692..3833927...54266663...764702068..11301659452
.1.101.125.819.7431.169601.2382399.54266663.1239155011.27405626123.629168904793
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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) = a(n-1) +3*a(n-2) -2*a(n-4) for n>5
k=3: [order 9] for n>13
k=4: [order 34]
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..0. .0..0..0..0. .0..0..1..1. .0..0..0..0
..0..0..1..1. .1..1..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..0
..1..0..1..1. .1..1..1..1. .1..1..1..1. .0..1..1..0. .0..1..0..0
..0..0..1..1. .0..0..0..0. .1..1..1..1. .0..0..1..1. .0..0..0..0
..0..0..1..1. .0..0..0..0. .0..1..1..0. .0..0..1..1. .0..0..0..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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