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A298294
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 6 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 69, 26, 26, 69, 32, 64, 137, 43, 46, 43, 137, 64, 128, 301, 72, 130, 130, 72, 301, 128, 256, 705, 115, 233, 308, 233, 115, 705, 256, 512, 1461, 189, 448, 515, 515, 448, 189, 1461, 512, 1024, 3193, 318, 877, 1084
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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....2048....4096
...2....7..13...29...69..137...301...705...1461...3193....7373...15729...34405
...4...13..20...26...43...72...115...189....318....526.....874....1473....2482
...8...29..26...46..130..233...448...877...1605...3284....6774...13516...26780
..16...69..43..130..308..515..1084..2374...4754..10042...21207...44405...93926
..32..137..72..233..515..990..1798..4079...9026..18246...39612...86150..184768
..64..301.115..448.1084.1798..4679.10688..22503..53875..123435..278930..642076
.128..705.189..877.2374.4079.10688.26963..60768.151924..370070..871422.2153007
.256.1461.318.1605.4754.9026.22503.60768.153319.389464.1009970.2538759.6516314
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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) = 3*a(n-1) -2*a(n-2) +8*a(n-3) -20*a(n-4) +8*a(n-5) for n>6
k=3: [order 17] for n>19
k=4: [order 67] for n>70
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EXAMPLE
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Some solutions for n=7 k=4
..0..1..0..1. .0..0..0..1. .0..1..1..0. .0..0..1..0. .0..0..1..0
..0..0..0..1. .1..1..1..0. .0..0..1..0. .1..1..1..0. .1..0..1..0
..0..0..1..0. .0..1..1..0. .1..1..1..0. .0..1..0..1. .0..0..1..0
..1..0..0..1. .1..0..1..0. .0..1..0..1. .0..1..0..1. .1..1..1..1
..0..0..0..0. .1..0..1..1. .0..1..0..1. .0..1..0..1. .0..1..0..0
..1..1..1..1. .1..0..1..1. .1..1..1..0. .1..0..0..0. .0..1..0..1
..0..0..0..0. .1..0..1..0. .0..0..1..0. .1..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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