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A316552
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 7 or 8 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 10, 17, 8, 13, 35, 17, 17, 35, 13, 21, 61, 36, 42, 36, 61, 21, 34, 127, 69, 89, 89, 69, 127, 34, 55, 265, 129, 187, 251, 187, 129, 265, 55, 89, 507, 260, 430, 621, 621, 430, 260, 507, 89, 144, 1013, 544, 1046, 1568, 1811, 1568, 1046, 544
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OFFSET
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1,2
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COMMENTS
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Table starts
..1...2...3....5.....8....13.....21......34......55.......89.......144
..2...5...7...17....35....61....127.....265.....507.....1013......2071
..3...7..10...17....36....69....129.....260.....544.....1125......2348
..5..17..17...42....89...187....430....1046....2407.....5706.....13873
..8..35..36...89...251...621...1568....4269...11869....33451.....95326
.13..61..69..187...621..1811...5265...17004...54443...174625....570128
.21.127.129..430..1568..5265..18978...73409..276005..1055277...4099795
.34.265.260.1046..4269.17004..73409..336604.1492856..6793881..31252764
.55.507.544.2407.11869.54443.276005.1492856.7870292.42144065.228096346
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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) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5
k=3: [order 15]
k=4: [order 45] for n>48
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..0. .0..1..1..0. .0..0..0..0. .0..0..0..0
..0..1..0..0. .1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .1..1..1..1. .1..1..0..0. .0..1..0..0. .0..0..0..0
..1..1..1..0. .1..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..1
..0..1..1..1. .1..1..0..0. .0..1..1..0. .0..0..0..0. .0..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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