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A298444
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
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7
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 11, 2, 1, 1, 5, 2, 2, 5, 1, 1, 9, 27, 7, 27, 9, 1, 1, 22, 36, 34, 34, 36, 22, 1, 1, 45, 86, 105, 214, 105, 86, 45, 1, 1, 101, 162, 406, 1270, 1270, 406, 162, 101, 1, 1, 218, 368, 1504, 3963, 10681, 3963, 1504, 368, 218, 1, 1, 477, 727, 6183
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OFFSET
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1,12
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COMMENTS
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Table starts
.1...1...1....1......1.......1.........1..........1............1.............1
.1...1...1....2......5.......9........22.........45..........101...........218
.1...1..11....2.....27......36........86........162..........368...........727
.1...2...2....7.....34.....105.......406.......1504.........6183.........25013
.1...5..27...34....214....1270......3963......22290.......109407........575051
.1...9..36..105...1270...10681.....72509.....692536......6184710......57152783
.1..22..86..406...3963...72509....610525....9392919....119508030....1732328018
.1..45.162.1504..22290..692536...9392919..240137045...5101146140..120394407026
.1.101.368.6183.109407.6184710.119508030.5101146140.176490627544.6773268608554
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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) -2*a(n-4) for n>5
k=3: [order 12] for n>13
k=4: [order 34] for n>36
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..0. .0..0..1..1. .0..1..1..1. .0..0..1..1. .0..0..1..1
..1..1..1..1. .0..0..1..1. .1..1..1..1. .0..0..1..1. .0..0..1..1
..1..0..1..0. .0..0..1..0. .1..1..0..0. .1..0..1..1. .0..1..1..1
..1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1
..0..1..1..1. .1..1..1..1. .0..0..0..1. .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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