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A299561
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
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7
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1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 18, 5, 18, 1, 1, 31, 15, 15, 31, 1, 1, 65, 21, 34, 21, 65, 1, 1, 130, 57, 77, 77, 57, 130, 1, 1, 253, 121, 230, 348, 230, 121, 253, 1, 1, 519, 289, 734, 1094, 1094, 734, 289, 519, 1, 1, 1018, 747, 2261, 3919, 4315, 3919, 2261, 747, 1018, 1
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OFFSET
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1,5
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COMMENTS
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Table starts
.1...1...1....1.....1......1.......1........1.........1.........1..........1
.1...5...7...18....31.....65.....130......253.......519......1018.......2055
.1...7...5...15....21.....57.....121......289.......747......1901.......5017
.1..18..15...34....77....230.....734.....2261......7050.....22143......69461
.1..31..21...77...348...1094....3919....13977.....49728....182756.....669766
.1..65..57..230..1094...4315...18032....75491....325547...1416774....6187701
.1.130.121..734..3919..18032...88551...451972...2321249..12137569...63355517
.1.253.289.2261.13977..75491..451972..2753155..16947296.105906482..660212203
.1.519.747.7050.49728.325547.2321249.16947296.124402861.927664758.6913834651
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..219
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
k=3: [order 19] for n>20
k=4: [order 72] for n>73
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EXAMPLE
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Some solutions for n=6 k=6
..0..0..0..1..1..1. .0..1..1..0..1..1. .0..0..0..0..1..0. .0..0..1..1..0..0
..0..1..1..0..0..1. .1..1..0..0..1..1. .0..0..0..0..1..1. .1..0..1..1..0..1
..0..1..1..1..0..1. .0..0..0..0..0..0. .0..0..0..0..1..0. .0..0..0..0..0..0
..0..1..1..1..1..0. .1..0..0..0..0..1. .1..1..1..1..1..1. .1..1..1..1..1..1
..0..1..1..1..1..0. .0..0..0..0..1..1. .0..1..0..0..0..0. .1..1..1..1..1..1
..0..0..0..0..0..0. .1..0..1..0..1..0. .1..1..0..0..0..0. .1..1..1..1..1..1
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CROSSREFS
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Column 2 is A297937.
Sequence in context: A297943 A298554 A298727 * A298382 A299249 A299458
Adjacent sequences: A299558 A299559 A299560 * A299562 A299563 A299564
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Feb 12 2018
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STATUS
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approved
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