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A299567
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
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6
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0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 52, 57, 52, 3, 5, 174, 222, 222, 174, 5, 8, 604, 808, 965, 808, 604, 8, 13, 2048, 3124, 4342, 4342, 3124, 2048, 13, 21, 6948, 11807, 20044, 24588, 20044, 11807, 6948, 21, 34, 23652, 44846, 91193, 140401, 140401, 91193, 44846
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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
..1.....4.....18......52......174.......604.......2048........6948........23652
..1....18.....57.....222......808......3124......11807.......44846.......170350
..2....52....222.....965.....4342.....20044......91193......417122......1909312
..3...174....808....4342....24588....140401.....792454.....4505710.....25597272
..5...604...3124...20044...140401....997212....6974944....49037025....345316723
..8..2048..11807...91193...792454...6974944...60087975...521019836...4532637754
.13..6948..44846..417122..4505710..49037025..521019836..5576669621..59935963606
.21.23652.170350.1909312.25597272.345316723.4532637754.59935963606.796438022548
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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) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6
k=3: [order 19] for n>20
k=4: [order 67] for n>70
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1
..0..0..0..1. .0..0..0..0. .0..0..0..1. .1..1..1..1. .0..0..0..1
..0..0..0..1. .0..0..0..0. .0..0..0..1. .1..1..1..1. .0..0..0..1
..0..0..1..0. .0..0..0..0. .0..0..0..1. .1..1..1..1. .1..1..1..1
..1..1..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1. .1..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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