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A298560
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.
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6
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0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 52, 56, 52, 3, 5, 174, 219, 219, 174, 5, 8, 604, 796, 956, 796, 604, 8, 13, 2048, 3079, 4304, 4304, 3079, 2048, 13, 21, 6948, 11614, 19843, 24364, 19843, 11614, 6948, 21, 34, 23652, 44076, 90153, 138774, 138774, 90153, 44076
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OFFSET
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1,5
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COMMENTS
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Table starts
..0.....1......1.......2........3.........5..........8..........13...........21
..1.....4.....18......52......174.......604.......2048........6948........23652
..1....18.....56.....219......796......3079......11614.......44076.......167210
..2....52....219.....956.....4304.....19843......90153......411915......1883419
..3...174....796....4304....24364....138774.....781071.....4432262.....25124403
..5...604...3079...19843...138774....983554....6852589....48019258....337105690
..8..2048..11614...90153...781071...6852589...58699120...506226692...4381689438
.13..6948..44076..411915..4432262..48019258..506226692..5376664548..57373679100
.21.23652.167210.1883419.25124403.337105690.4381689438.57373679100.755503324152
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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) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6
k=3: [order 20] for n>21
k=4: [order 67] for n>70
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..0. .0..0..0..1. .0..0..1..1. .0..1..0..0. .0..0..1..1
..0..0..1..1. .0..0..0..1. .1..0..0..0. .1..0..1..1. .1..1..1..0
..0..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..1..1. .1..1..0..1
..1..0..0..0. .1..1..0..1. .1..0..0..0. .0..1..1..1. .1..1..1..0
..1..0..0..0. .0..0..0..0. .1..0..0..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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