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A306053
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 6 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, 21, 21, 8, 16, 49, 45, 49, 16, 32, 120, 142, 142, 120, 32, 64, 293, 439, 458, 439, 293, 64, 128, 719, 1261, 1962, 1962, 1261, 719, 128, 256, 1774, 3826, 6604, 12349, 6604, 3826, 1774, 256, 512, 4389, 11770, 22446, 66149, 66149, 22446, 11770
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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
...2....8....21.....49.....120.......293........719.........1774..........4389
...4...21....45....142.....439......1261.......3826........11770.........35152
...8...49...142....458....1962......6604......22446........86464........311891
..16..120...439...1962...12349.....66149.....321707......1803281.......9990733
..32..293..1261...6604...66149....554682....3914486.....34263459.....301965791
..64..719..3826..22446..321707...3914486...36596835....458669749....5842600934
.128.1774.11770..86464.1803281..34263459..458669749...8395262149..162463649507
.256.4389.35152.311891.9990733.301965791.5842600934.162463649507.4973359586800
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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) = 3*a(n-1) +a(n-2) -4*a(n-3) -4*a(n-4) for n>5
k=3: [order 10] for n>12
k=4: [order 21] for n>25
k=5: [order 85] for n>89
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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..1..0. .0..0..1..1. .0..0..0..0
..0..1..1..0. .0..0..0..0. .1..1..0..0. .0..0..1..0. .1..1..1..1
..0..0..0..0. .0..1..0..0. .1..1..1..1. .0..0..0..0. .1..1..1..1
..0..0..1..0. .0..1..0..0. .0..0..1..1. .0..1..1..0. .1..1..1..0
..1..1..0..1. .0..0..0..0. .0..1..1..1. .1..0..0..0. .0..1..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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