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A318075
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 6, 4, 8, 10, 10, 8, 16, 20, 18, 20, 16, 32, 42, 41, 41, 42, 32, 64, 89, 81, 73, 81, 89, 64, 128, 190, 179, 149, 149, 179, 190, 128, 256, 407, 404, 372, 316, 372, 404, 407, 256, 512, 873, 893, 861, 854, 854, 861, 893, 873, 512, 1024, 1874, 2000, 2016, 2195
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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.......1024
...2...6...10...20....42.....89....190.....407......873......1874.......4024
...4..10...18...41....81....179....404.....893.....2000......4516......10125
...8..20...41...73...149....372....861....2016.....4901.....11698......27986
..16..42...81..149...316....854...2195....5752....15565.....41364.....110930
..32..89..179..372...854...3029...9966...31057...102906....339938....1115341
..64.190..404..861..2195...9966..46884..184156...819263...3703730...15865269
.128.407..893.2016..5752..31057.184156..935951..5311510..30435406..167286074
.256.873.2000.4901.15565.102906.819263.5311510.38183961.285095330.2029620744
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..420
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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) +a(n-2) -a(n-3) -a(n-4) for n>6
k=3: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -3*a(n-4) -6*a(n-5) +6*a(n-6) for n>10
k=4: [order 18] for n>21
k=5: [order 29] for n>33
k=6: [order 56] for n>61
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..0. .0..0..0..1. .0..0..0..0. .0..0..1..1. .0..1..1..0
..1..1..0..1. .0..0..1..0. .0..1..1..0. .0..0..1..1. .1..1..0..0
..1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1. .1..0..0..0
..1..1..1..1. .0..1..0..0. .0..0..0..1. .0..0..1..1. .0..0..0..0
..1..1..1..0. .1..0..0..1. .0..0..1..1. .0..0..1..1. .1..1..1..1
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CROSSREFS
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Column 1 is A000079(n-1).
Column 2 is A317759.
Sequence in context: A089002 A097089 A317764 * A318343 A318024 A320409
Adjacent sequences: A318072 A318073 A318074 * A318076 A318077 A318078
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Aug 15 2018
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STATUS
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approved
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