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A298775
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
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5
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0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 25, 25, 23, 5, 8, 49, 47, 78, 47, 49, 8, 13, 99, 109, 233, 233, 109, 99, 13, 21, 189, 245, 779, 682, 779, 245, 189, 21, 34, 383, 545, 2359, 2603, 2603, 2359, 545, 383, 34, 55, 777, 1253, 7024, 11657, 11320, 11657, 7024
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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..........34
..1...3....7....13.....23......49.......99.......189........383.........777
..1...7...15....25.....47.....109......245.......545.......1253........2859
..2..13...25....78....233.....779.....2359......7024......21572.......66763
..3..23...47...233....682....2603....11657.....39908.....149791......617528
..5..49..109...779...2603...11320....61333....284618....1376511.....6959439
..8..99..245..2359..11657...61333...484813...2887678...18497464...127977516
.13.189..545..7024..39908..284618..2887678..22160831..186728055..1683257109
.21.383.1253.21572.149791.1376511.18497464.186728055.2093453587.24925712914
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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 12] for n>13
k=4: [order 62] for n>65
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EXAMPLE
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Some solutions for n=6 k=5
..0..0..0..1..0. .0..1..0..0..0. .0..1..1..1..0. .0..0..0..0..0
..1..0..0..0..1. .1..0..0..0..1. .1..0..0..0..1. .1..0..0..0..1
..0..1..1..1..0. .0..1..1..1..0. .1..0..0..0..1. .0..1..1..1..0
..0..1..1..1..0. .0..1..1..1..0. .1..0..0..0..1. .0..1..1..1..0
..0..1..1..1..0. .0..1..1..1..0. .0..1..1..1..0. .0..1..1..1..0
..1..0..0..0..1. .1..0..0..0..1. .1..1..1..0..1. .1..0..0..0..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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