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A298895
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
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7
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0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 1, 2, 0, 0, 11, 4, 4, 11, 0, 0, 13, 4, 11, 4, 13, 0, 0, 34, 11, 31, 31, 11, 34, 0, 0, 65, 26, 80, 219, 80, 26, 65, 0, 0, 123, 66, 229, 579, 579, 229, 66, 123, 0, 0, 266, 171, 681, 1858, 2963, 1858, 681, 171, 266, 0, 0, 499, 462, 1969, 8891, 12224
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OFFSET
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1,8
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COMMENTS
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Table starts
.0...0...0....0.....0......0.......0........0.........0..........0............0
.0...1...3....2....11.....13......34.......65.......123........266..........499
.0...3...1....4.....4.....11......26.......66.......171........462.........1248
.0...2...4...11....31.....80.....229......681......1969.......5973........18031
.0..11...4...31...219....579....1858.....8891.....34212.....128103.......538967
.0..13..11...80...579...2963...12224....72620....426475....2284203.....12768382
.0..34..26..229..1858..12224...74725...547497...4012035...28805843....209118279
.0..65..66..681..8891..72620..547497..5719782..54423404..502721390...4804572705
.0.123.171.1969.34212.426475.4012035.54423404.724538480.8857192378.112203393143
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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)
k=3: [order 17] for n>18
k=4: [order 58] for n>59
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EXAMPLE
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Some solutions for n=7 k=4
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..1..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
..1..1..1..1. .0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1
..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..0..0..1. .1..0..0..1
..0..0..0..0. .1..1..1..1. .1..1..1..1. .0..1..0..1. .0..1..1..0
..0..0..0..0. .1..1..1..1. .1..1..1..1. .0..0..1..1. .0..0..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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