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A298554
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5 or 7 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, 4, 18, 1, 1, 31, 14, 14, 31, 1, 1, 65, 16, 33, 16, 65, 1, 1, 130, 51, 74, 74, 51, 130, 1, 1, 253, 104, 226, 341, 226, 104, 253, 1, 1, 519, 262, 716, 1073, 1073, 716, 262, 519, 1, 1, 1018, 689, 2211, 3822, 4157, 3822, 2211, 689, 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...4...14....16.....51.....104......262.......689......1784.......4767
.1..18..14...33....74....226.....716.....2211......6851.....21462......67050
.1..31..16...74...341...1073....3822....13570.....48112....176011.....641370
.1..65..51..226..1073...4157...17378....72567....310925...1345213....5838677
.1.130.104..716..3822..17378...85227...430934...2190786..11366897...58786296
.1.253.262.2211.13570..72567..430934..2586208..15726159..97403128..600617339
.1.519.689.6851.48112.310925.2190786.15726159.113602418.837791825.6166852815
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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)
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=7 k=4
..0..1..0..1. .0..0..1..0. .0..0..1..0. .0..0..1..1. .0..0..1..1
..0..0..0..0. .1..0..1..1. .1..0..1..1. .0..0..1..0. .1..0..1..1
..0..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1. .0..0..0..0
..0..1..1..1. .1..0..0..1. .1..0..0..1. .0..1..1..0. .1..0..0..1
..1..0..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1. .0..0..0..0
..1..1..0..0. .1..1..0..1. .1..1..0..1. .0..0..1..0. .1..1..0..1
..0..1..1..0. .0..1..0..0. .1..1..0..0. .0..0..1..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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