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A296827
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T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2, 3 or 4 king-move neighboring 1s.
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8
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1, 1, 1, 1, 6, 1, 1, 21, 21, 1, 1, 56, 94, 56, 1, 1, 178, 352, 352, 178, 1, 1, 609, 2133, 2272, 2133, 609, 1, 1, 1997, 11930, 24367, 24367, 11930, 1997, 1, 1, 6511, 60772, 214243, 510086, 214243, 60772, 6511, 1, 1, 21494, 326592, 1814475, 8721984, 8721984
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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.....6......21........56.........178...........609.............1997
.1....21......94.......352........2133.........11930............60772
.1....56.....352......2272.......24367........214243..........1814475
.1...178....2133.....24367......510086.......8721984........139963008
.1...609...11930....214243.....8721984.....267542809.......7478283799
.1..1997...60772...1814475...139963008....7478283799.....364592446431
.1..6511..326592..16388418..2411616295..232289837440...20210620228470
.1.21494.1772900.145662798.41118326040.7106285417721.1091459884529060
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..180
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +5*a(n-3) -2*a(n-4) -10*a(n-5) -8*a(n-6)
k=3: [order 16]
k=4: [order 35]
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EXAMPLE
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Some solutions for n=4 k=4
..1..1..1..0. .0..1..1..1. .1..1..0..1. .0..1..0..0. .1..1..1..0
..0..1..0..0. .1..0..0..1. .1..0..1..1. .1..1..0..0. .1..0..1..0
..0..0..1..0. .1..0..0..1. .1..0..1..0. .0..0..1..0. .0..1..1..0
..0..1..1..0. .0..1..1..0. .0..1..0..0. .0..1..1..0. .0..0..1..0
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CROSSREFS
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Sequence in context: A203954 A060972 A144066 * A056941 A157638 A347975
Adjacent sequences: A296824 A296825 A296826 * A296828 A296829 A296830
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Dec 21 2017
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STATUS
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approved
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