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A298712
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.
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7
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0, 1, 1, 0, 4, 0, 1, 3, 3, 1, 0, 13, 0, 13, 0, 1, 32, 2, 2, 32, 1, 0, 53, 6, 11, 6, 53, 0, 1, 125, 20, 32, 32, 20, 125, 1, 0, 386, 22, 87, 781, 87, 22, 386, 0, 1, 727, 92, 110, 1354, 1354, 110, 92, 727, 1, 0, 1601, 206, 385, 2409, 3950, 2409, 385, 206, 1601, 0, 1, 4568, 460, 908
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OFFSET
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1,5
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COMMENTS
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Table starts
.0...1...0...1......0......1.......0........1.........0..........1...........0
.1...4...3..13.....32.....53.....125......386.......727.......1601........4568
.0...3...0...2......6.....20......22.......92.......206........460........1176
.1..13...2..11.....32.....87.....110......385.......908.......2760........6454
.0..32...6..32....781...1354....2409....34250....109459.....294045.....2120905
.1..53..20..87...1354...3950....9586....92375....384519....1468344.....9531019
.0.125..22.110...2409...9586...17377...241249...1201122....6055242....45702804
.1.386..92.385..34250..92375..241249..8695221..49691754..274634548..4587455345
.0.727.206.908.109459.384519.1201122.49691754.359275256.2514115870.49068141912
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-2)
k=2: a(n) = a(n-1) +a(n-2) +8*a(n-3) -16*a(n-5)
k=3: [order 17] for n>18
k=4: [order 70]
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..1. .0..0..1..0. .0..0..1..1. .0..1..1..1. .0..1..1..1
..0..1..0..1. .0..0..1..0. .0..0..0..0. .1..0..1..1. .1..0..1..1
..1..1..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
..0..1..0..1. .0..0..1..0. .0..0..1..1. .1..0..1..1. .0..1..1..1
..0..1..0..1. .0..0..0..1. .0..0..0..0. .1..0..1..1. .1..0..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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