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A298396
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
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7
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0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 29, 29, 23, 5, 8, 49, 63, 112, 63, 49, 8, 13, 99, 167, 432, 432, 167, 99, 13, 21, 189, 473, 1915, 2231, 1915, 473, 189, 21, 34, 383, 1205, 7556, 13271, 13271, 7556, 1205, 383, 34, 55, 777, 3161, 29657, 81019, 117184
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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...3....7.....13......23.......49.........99.........189...........383
..1...7...15.....29......63......167........473........1205..........3161
..2..13...29....112.....432.....1915.......7556.......29657........123601
..3..23...63....432....2231....13271......81019......454822.......2647771
..5..49..167...1915...13271...117184....1142217.....9792821......87882289
..8..99..473...7556...81019..1142217...16510708...212408711....2962142231
.13.189.1205..29657..454822..9792821..212408711..4149393799...87858962506
.21.383.3161.123601.2647771.87882289.2962142231.87858962506.2858791588717
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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) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5
k=3: [order 15] for n>17
k=4: [order 68] for n>71
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..0. .0..0..1..0. .0..1..0..1. .0..0..0..1. .0..0..0..0
..1..0..0..1. .1..1..0..1. .0..0..1..0. .1..1..1..0. .1..0..0..1
..0..1..0..0. .0..0..0..1. .0..0..1..1. .0..1..1..1. .1..1..1..1
..1..0..0..0. .1..0..0..1. .1..0..1..1. .0..1..0..0. .1..1..0..0
..0..1..1..0. .1..0..1..0. .0..1..0..1. .1..0..1..1. .1..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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