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A299458
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
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7
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1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 18, 7, 18, 1, 1, 31, 19, 19, 31, 1, 1, 65, 35, 48, 35, 65, 1, 1, 130, 95, 175, 175, 95, 130, 1, 1, 253, 223, 508, 1015, 508, 223, 253, 1, 1, 519, 571, 1522, 3514, 3514, 1522, 571, 519, 1, 1, 1018, 1535, 5065, 14409, 19041, 14409, 5065, 1535
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OFFSET
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1,5
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COMMENTS
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Table starts
.1...1....1.....1......1.......1........1.........1...........1............1
.1...5....7....18.....31......65......130.......253.........519.........1018
.1...7....7....19.....35......95......223.......571........1535.........4091
.1..18...19....48....175.....508.....1522......5065.......16968........56041
.1..31...35...175...1015....3514....14409.....69402......304094......1294490
.1..65...95...508...3514...19041...101878....624052.....3827796.....22241786
.1.130..223..1522..14409..101878...750083...6104533....48998539....384601868
.1.253..571..5065..69402..624052..6104533..67847199...723450111...7524339497
.1.519.1535.16968.304094.3827796.48998539.723450111.10455199270.145448283457
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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) for n>5
k=3: [order 18] for n>19
k=4: [order 70] for n>71
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EXAMPLE
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Some solutions for n=6 k=6
..0..0..0..0..1..1. .0..0..0..1..0..1. .0..0..0..0..1..0. .0..0..1..1..0..0
..0..0..0..0..1..1. .0..0..0..1..1..1. .0..0..0..0..1..1. .1..0..0..1..0..0
..0..0..0..0..1..1. .0..0..0..1..0..1. .0..0..0..0..0..0. .0..0..1..1..1..1
..0..0..0..0..0..0. .0..0..0..0..0..0. .1..1..1..1..0..0. .1..1..1..1..0..1
..1..1..1..0..1..0. .1..1..0..0..1..0. .0..1..0..0..1..1. .1..1..1..0..0..0
..0..1..0..0..1..1. .0..1..1..0..1..1. .1..1..1..0..1..0. .1..1..1..0..1..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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