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A316815
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 227, 128, 16, 32, 512, 1603, 1603, 512, 32, 64, 2048, 11339, 19816, 11339, 2048, 64, 128, 8192, 80196, 246196, 246196, 80196, 8192, 128, 256, 32768, 567185, 3056047, 5391628, 3056047, 567185, 32768, 256, 512, 131072
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OFFSET
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1,2
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COMMENTS
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Table starts
...1......2........4..........8............16..............32................64
...2......8.......32........128...........512............2048..............8192
...4.....32......227.......1603.........11339...........80196............567185
...8....128.....1603......19816........246196.........3056047..........37935501
..16....512....11339.....246196.......5391628.......117897523........2578023456
..32...2048....80196....3056047.....117897523......4537910922......174669587289
..64...8192...567185...37935501....2578023456....174669587289....11834952392431
.128..32768..4011528..470942175...56382210217...6724877943937...802147875327622
.256.131072.28372197.5846244187.1233022160942.258886627124646.54360782611063950
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 6*a(n-1) +10*a(n-2) -7*a(n-3) -64*a(n-4) -51*a(n-5) for n>6
k=4: [order 17] for n>18
k=5: [order 62] for n>63
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..1. .0..0..1..1. .0..0..0..1. .0..0..0..0. .0..0..0..1
..1..1..1..0. .0..1..0..1. .1..1..1..1. .0..1..1..0. .0..1..0..1
..1..0..0..1. .1..1..1..1. .0..1..0..1. .1..0..1..1. .0..0..1..1
..0..0..1..1. .1..1..1..1. .1..0..0..0. .1..0..0..0. .0..0..0..0
..1..1..1..1. .1..1..1..1. .1..1..1..0. .1..1..0..0. .0..1..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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