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A299675
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 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, 26, 26, 8, 16, 88, 94, 88, 16, 32, 298, 372, 372, 298, 32, 64, 1012, 1512, 2009, 1512, 1012, 64, 128, 3440, 6133, 12076, 12076, 6133, 3440, 128, 256, 11700, 24742, 69614, 131420, 69614, 24742, 11700, 256, 512, 39804, 100035, 398314
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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
...2.....8.....26.......88........298........1012..........3440...........11700
...4....26.....94......372.......1512........6133.........24742..........100035
...8....88....372.....2009......12076.......69614........398314.........2305246
..16...298...1512....12076.....131420.....1223912......11202963.......109221761
..32..1012...6133....69614....1223912....17105490.....231836591......3441737079
..64..3440..24742...398314...11202963...231836591....4670821739....105367758168
.128.11700.100035..2305246..109221761..3441737079..105367758168...3777344294506
.256.39804.404608.13349305.1053093991.50285500321.2312626806147.130056973753183
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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) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5)
k=3: [order 18] for n>19
k=4: [order 65] for n>66
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..0..0..0. .0..0..1..1
..0..0..0..0. .0..0..0..0. .0..1..1..1. .0..0..0..0. .1..0..0..0
..1..0..0..1. .1..0..0..1. .1..1..1..0. .0..0..1..1. .0..0..0..0
..1..0..0..0. .0..0..0..0. .0..1..1..1. .0..0..0..1. .0..1..0..0
..0..0..1..1. .0..1..0..1. .0..1..0..0. .1..1..0..1. .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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