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A316620
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
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5
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1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 13, 13, 1, 1, 26, 21, 21, 26, 1, 1, 49, 29, 26, 29, 49, 1, 1, 99, 58, 70, 70, 58, 99, 1, 1, 194, 120, 139, 189, 139, 120, 194, 1, 1, 387, 250, 287, 468, 468, 287, 250, 387, 1, 1, 773, 515, 625, 1446, 1916, 1446, 625, 515, 773, 1, 1, 1538
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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
.1...4...7...13....26....49.....99.....194......387.......773......1538
.1...7..13...21....29....58....120.....250......515......1100......2302
.1..13..21...26....70...139....287.....625.....1484......3197......7321
.1..26..29...70...189...468...1446....3769....11196.....32714.....93764
.1..49..58..139...468..1916...5428...18126....66146....225773....773853
.1..99.120..287..1446..5428..20777...86855...376999...1555947...6605299
.1.194.250..625..3769.18126..86855..476965..2572180..13348093..71288692
.1.387.515.1484.11196.66146.376999.2572180.16700783.105494740.692447139
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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=5 k=4
..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..1..0..0. .0..1..1..0
..1..1..0..0. .1..1..1..1. .0..0..1..1. .1..0..1..1. .0..1..0..1
..1..0..0..0. .1..0..0..1. .0..0..0..1. .0..1..1..1. .1..0..0..1
..1..0..1..1. .1..0..0..1. .1..1..0..1. .1..0..1..1. .0..1..0..1
..0..1..1..0. .1..0..0..1. .0..1..1..0. .0..1..0..0. .0..1..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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