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A316420
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 14, 9, 16, 32, 22, 27, 27, 22, 32, 64, 45, 66, 93, 66, 45, 64, 128, 101, 180, 287, 287, 180, 101, 128, 256, 218, 484, 1009, 1265, 1009, 484, 218, 256, 512, 477, 1261, 3496, 5695, 5695, 3496, 1261, 477, 512, 1024, 1041, 3346, 11962
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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........128.........256..........512
...2...4....5.....9.....22......45......101........218.........477.........1041
...4...5...14....27.....66.....180......484.......1261........3346.........8912
...8...9...27....93....287....1009.....3496......11962.......41160.......142076
..16..22...66...287...1265....5695....25312.....112499......501646......2235513
..32..45..180..1009...5695...33380...192752....1116462.....6489620.....37702431
..64.101..484..3496..25312..192752..1459806...11066456....84120192....639206832
.128.218.1261.11962.112499.1116462.11066456..110043463..1095070964..10891632449
.256.477.3346.41160.501646.6489620.84120192.1095070964.14254922771.185426707377
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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) = a(n-1) +3*a(n-2) -2*a(n-4) for n>6
k=3: a(n) = a(n-1) +3*a(n-2) +4*a(n-3) +2*a(n-4) -3*a(n-5) -9*a(n-6) -6*a(n-7) for n>10
k=4: [order 19] for n>23
k=5: [order 43] for n>49
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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..0..1..0. .0..0..1..1. .0..1..0..0
..0..0..0..0. .1..0..1..0. .0..0..0..0. .0..0..1..1. .0..0..0..1
..0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0. .1..0..0..0
..0..0..0..1. .0..0..0..1. .0..1..0..1. .0..0..0..0. .0..0..1..0
..0..1..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..0. .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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