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A299612
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
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6
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0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 19, 19, 23, 5, 8, 49, 23, 40, 23, 49, 8, 13, 95, 34, 85, 85, 34, 95, 13, 21, 177, 63, 173, 179, 173, 63, 177, 21, 34, 359, 96, 322, 453, 453, 322, 96, 359, 34, 55, 705, 147, 635, 1006, 1223, 1006, 635, 147, 705, 55, 89, 1351
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OFFSET
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1,5
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COMMENTS
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Table starts
..0...1...1....2....3.....5......8......13......21.......34........55
..1...3...7...13...23....49.....95.....177.....359......705......1351
..1...7..15...19...23....34.....63......96.....147......233.......368
..2..13..19...40...85...173....322.....635....1325.....2806......5877
..3..23..23...85..179...453...1006....2523....6002....14802.....36299
..5..49..34..173..453..1223...3286....9873...28227....86428....253623
..8..95..63..322.1006..3286..13490...49047..183585...713699...2714170
.13.177..96..635.2523..9873..49047..231838.1084038..5339757..25938953
.21.359.147.1325.6002.28227.183585.1084038.6506278.41165944.255972254
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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) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6
k=3: [order 18] for n>19
k=4: [order 72] for n>73
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EXAMPLE
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Some solutions for n=6 k=6
..0..1..1..1..0..1. .0..1..1..0..0..0. .0..1..0..1..0..0. .0..1..0..1..1..0
..0..0..1..1..1..0. .0..0..0..0..0..1. .0..1..0..1..0..1. .0..1..0..0..0..0
..1..1..1..1..1..1. .0..0..0..0..1..0. .1..1..1..1..1..1. .0..1..0..0..0..0
..0..0..1..1..1..1. .1..0..0..0..0..1. .0..0..1..1..1..1. .1..0..0..0..0..1
..1..1..1..0..0..1. .0..1..0..1..0..1. .1..1..1..1..1..0. .1..0..1..0..0..1
..0..0..1..0..1..1. .0..1..0..1..0..0. .0..0..1..1..0..1. .0..1..0..1..0..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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