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A298924
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
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7
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0, 1, 1, 0, 4, 0, 1, 4, 4, 1, 0, 8, 1, 8, 0, 1, 32, 2, 2, 32, 1, 0, 32, 3, 3, 3, 32, 0, 1, 64, 5, 7, 7, 5, 64, 1, 0, 256, 8, 6, 9, 6, 8, 256, 0, 1, 256, 16, 9, 12, 12, 9, 16, 256, 1, 0, 512, 21, 20, 17, 19, 17, 20, 21, 512, 0, 1, 2048, 34, 22, 41, 22, 22, 41, 22, 34, 2048, 1, 0, 2048, 55, 35, 42
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OFFSET
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1,5
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COMMENTS
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Table starts
.0...1..0..1..0..1..0...1...0...1....0....1....0.....1.....0.....1......0
.1...4..4..8.32.32.64.256.256.512.2048.2048.4096.16384.16384.32768.131072
.0...4..1..2..3..5..8..16..21..34...55...89..144...236...377...610....987
.1...8..2..3..7..6..9..20..22..35...59...90..145...240...378...611....991
.0..32..3..7..9.12.17..41..42..67..109..172..277...461...722..1167...1889
.1..32..5..6.12.19.22..48..53.103..169..272..446...863..1346..2395...4154
.0..64..8..9.17.22.31..83..92.172..309..549..923..1830..3021..5580..10091
.1.256.16.20.41.48.83.199.225.460..943.1570.2795..5933.10113.19462..37621
.0.256.21.22.42.53.92.225.330.644.1348.2306.4339..9315.17574.35170..70446
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-2)
k=2: a(n) = 8*a(n-3)
k=3: a(n) = a(n-1) +a(n-2) +a(n-6) -a(n-7) -a(n-8)
k=4: a(n) = a(n-1) +a(n-2) +a(n-6) -a(n-7) -a(n-8)
k=5: a(n) = a(n-1) +a(n-2) +a(n-6) -a(n-7) -a(n-8) for n>11
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..0. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
..0..0..0..0. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
..0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..0..0. .0..0..1..1
..1..1..1..1. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
..1..1..1..1. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
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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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