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A317429
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
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6
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1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 14, 21, 8, 13, 53, 32, 32, 53, 13, 21, 105, 75, 97, 75, 105, 21, 34, 237, 148, 279, 279, 148, 237, 34, 55, 577, 311, 640, 1097, 640, 311, 577, 55, 89, 1205, 687, 1666, 2891, 2891, 1666, 687, 1205, 89, 144, 2681, 1443, 4365, 8887, 9116
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OFFSET
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1,2
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COMMENTS
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Table starts
..1....2....3.....5.....8.....13......21.......34.......55........89........144
..2....5....9....21....53....105.....237......577.....1205......2681.......6349
..3....9...14....32....75....148.....311......687.....1443......3042.......6534
..5...21...32....97...279....640....1666.....4365....11025.....28226......72631
..8...53...75...279..1097...2891....8887....30029....89848....274792.....882160
.13..105..148...640..2891...9116...32359...125832...439409...1569243....5838001
.21..237..311..1666..8887..32359..135880...617692..2534229..10679366...46580215
.34..577..687..4365.30029.125832..617692..3452903.16763615..83384489..439271584
.55.1205.1443.11025.89848.439409.2534229.16763615.95798175.562775876.3505340437
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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) = a(n-1) +8*a(n-3) -4*a(n-4)
k=3: [order 12]
k=4: [order 40] for n>41
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..0. .0..0..1..1. .0..0..1..1. .0..1..1..0. .0..0..0..0
..1..1..0..1. .0..1..1..1. .0..1..1..1. .1..1..1..1. .0..0..0..0
..1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..1
..1..1..1..1. .1..1..1..0. .1..1..1..1. .0..1..1..1. .0..0..1..1
..1..1..1..1. .0..1..1..1. .1..1..1..0. .1..1..1..0. .0..1..1..1
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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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