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A305911
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T(n,k) = Number of n X k 0..1 arrays with every element unequal to 0, 1, 2, 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, 4, 4, 8, 14, 14, 8, 16, 28, 35, 28, 16, 32, 94, 98, 98, 94, 32, 64, 284, 358, 396, 358, 284, 64, 128, 752, 1124, 2075, 2075, 1124, 752, 128, 256, 2244, 3534, 9140, 15460, 9140, 3534, 2244, 256, 512, 6532, 11667, 40412, 86944, 86944, 40412, 11667, 6532
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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....4....14.....28.......94.......284........752........2244..........6532
...4...14....35.....98......358......1124.......3534.......11667.........37816
...8...28....98....396.....2075......9140......40412......189729........873060
..16...94...358...2075....15460.....86944.....505624.....3261562......20076871
..32..284..1124...9140....86944....595490....4408093....36427606.....282035936
..64..752..3534..40412...505624...4408093...42789430...473649265....4825821471
.128.2244.11667.189729..3261562..36427606..473649265..7157370110...96982248284
.256.6532.37816.873060.20076871.282035936.4825821471.96982248284.1710658272713
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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) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n > 6;
k=3: [order 15] for n > 16;
k=4: [order 69] for n > 70.
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EXAMPLE
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Some solutions for n=5, k=4
..0..1..1..1. .0..1..1..0. .0..1..1..1. .0..0..0..0. .0..0..0..1
..0..1..1..0. .0..0..0..0. .0..1..1..0. .0..0..0..1. .1..0..0..1
..1..1..1..1. .0..0..0..0. .1..1..1..0. .0..0..0..1. .0..0..0..0
..0..1..1..1. .1..1..0..0. .1..1..0..0. .0..0..1..1. .1..0..0..0
..1..1..0..0. .1..1..1..1. .1..0..1..0. .0..0..1..1. .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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