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A297986
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 6 king-move adjacent elements, with upper left element zero.
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8
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1, 1, 1, 1, 5, 1, 1, 6, 6, 1, 1, 17, 2, 17, 1, 1, 24, 5, 5, 24, 1, 1, 53, 7, 15, 7, 53, 1, 1, 94, 14, 23, 23, 14, 94, 1, 1, 173, 21, 43, 34, 43, 21, 173, 1, 1, 340, 41, 79, 61, 61, 79, 41, 340, 1, 1, 601, 70, 184, 105, 131, 105, 184, 70, 601, 1, 1, 1178, 129, 380, 222, 242, 242, 222
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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......1......1......1
.1...5..6..17..24...53...94..173..340...601..1178..2137...4056...7565..14086
.1...6..2...5...7...14...21...41...70...129...233...428....783...1445...2664
.1..17..5..15..23...43...79..184..380...830..1776..3815...8227..17737..38335
.1..24..7..23..34...61..105..222..428...948..1975..4162...8801..18972..40777
.1..53.14..43..61..131..242..530.1226..2701..5847.13187..30316..68963.156767
.1..94.21..79.105..242..444..935.1835..3921..8793.19694..44948.102048.235955
.1.173.41.184.222..530..935.1980.3832..8355.18941.40962..89009.197337.448014
.1.340.70.380.428.1226.1835.3832.6500.15690.33619.75185.159728.361567.821919
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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) = 3*a(n-2) +2*a(n-3) -2*a(n-4) for n>5
k=3: [order 11] for n>13
k=4: [order 22] for n>28
k=5: [order 37] for n>43
k=6: [order 76] for n>84
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EXAMPLE
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Some solutions for n=7 k=4
..0..0..1..1. .0..0..1..0. .0..0..1..0. .0..1..1..1. .0..0..0..0
..0..1..0..1. .0..1..1..1. .0..1..1..1. .0..0..1..0. .0..1..1..0
..1..0..1..0. .1..0..0..0. .1..0..0..0. .0..1..1..1. .1..0..1..0
..1..0..1..0. .0..1..1..0. .0..1..1..0. .1..0..0..0. .1..0..1..0
..1..0..1..0. .0..1..0..1. .0..0..1..0. .0..1..1..0. .1..0..1..0
..1..0..0..1. .1..0..0..1. .1..0..1..0. .0..1..0..1. .0..1..0..1
..1..1..1..1. .1..1..1..1. .1..1..0..0. .0..0..1..1. .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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