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A304302
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 5 or 8 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, 2, 2, 2, 3, 1, 3, 1, 3, 5, 8, 5, 5, 8, 5, 8, 5, 6, 4, 6, 5, 8, 13, 22, 14, 13, 13, 14, 22, 13, 21, 29, 22, 30, 62, 30, 22, 29, 21, 34, 60, 33, 43, 88, 88, 43, 33, 60, 34, 55, 121, 57, 129, 339, 237, 339, 129, 57, 121, 55, 89, 194, 97, 245, 888, 685, 685, 888, 245
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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.......55.......89.......144
..1..3..2...1....8....5....22.....29.....60.....121......194......425.......704
..1..2..3...5....6...14....22.....33.....57......97......159......255.......432
..2..1..5...4...13...30....43....129....245.....519.....1254.....2525......5707
..3..8..6..13...62...88...339....888...2108....6329....16064....43396....117393
..5..5.14..30...88..237...685...1827...4974...14425....38170...106811....300976
..8.22.22..43..339..685..2673..11690..31390..133744...470762..1540068...6102146
.13.29.33.129..888.1827.11690..47501.161251..821454..3119449.12780462..56341952
.21.60.57.245.2108.4974.31390.161251.555463.3235101.14367171.61271388.319305797
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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) = 3*a(n-2) +2*a(n-3) -2*a(n-4) for n>6
k=3: a(n) = a(n-2) +3*a(n-3) +2*a(n-4) -4*a(n-6) -2*a(n-7) -a(n-8) -2*a(n-9)
k=4: [order 15] for n>19
k=5: [order 32] for n>34
k=6: [order 64] for n>66
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..0. .0..0..0..0. .0..1..0..0. .0..0..1..0. .0..0..0..0
..1..0..0..0. .1..0..0..1. .0..0..0..1. .1..0..0..0. .1..0..0..1
..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..0..0
..1..0..0..1. .0..0..0..1. .0..0..0..1. .0..0..0..1. .1..0..0..0
..0..0..0..0. .0..1..0..0. .0..1..0..0. .0..1..0..0. .0..0..1..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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