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A300498
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 7, 4, 8, 18, 18, 8, 16, 50, 52, 50, 16, 32, 138, 143, 143, 138, 32, 64, 383, 412, 499, 412, 383, 64, 128, 1063, 1225, 1513, 1513, 1225, 1063, 128, 256, 2951, 3699, 4686, 5837, 4686, 3699, 2951, 256, 512, 8193, 11243, 14822, 19412, 19412, 14822, 11243
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OFFSET
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1,2
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COMMENTS
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Table starts
...1....2.....4......8.....16......32.......64.......128.......256........512
...2....7....18.....50....138.....383.....1063......2951......8193......22748
...4...18....52....143....412....1225.....3699.....11243.....34012.....102446
...8...50...143....499...1513....4686....14822.....46717....149232.....478952
..16..138...412...1513...5837...19412....66166....233796....816547....2856851
..32..383..1225...4686..19412...77582...291721...1136238...4513729...17926620
..64.1063..3699..14822..66166..291721..1296506...5589526..24694845..110652439
.128.2951.11243..46717.233796.1136238..5589526..28067098.138863892..695711878
.256.8193.34012.149232.816547.4513729.24694845.138863892.789286221.4445350963
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2) +a(n-3) +a(n-4) -2*a(n-5) -a(n-6)
k=3: [order 24] for n>25
k=4: [order 83] for n>86
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..0. .0..1..0..1. .0..0..1..1. .0..1..1..1. .0..0..1..1
..1..0..1..1. .1..0..1..0. .1..0..1..0. .1..0..0..0. .1..0..0..1
..0..1..0..1. .0..1..0..1. .0..1..1..1. .1..1..1..0. .1..1..0..0
..0..1..0..0. .1..0..1..1. .1..1..0..0. .0..0..1..0. .0..0..0..1
..0..1..1..1. .0..1..1..1. .0..1..0..1. .1..0..1..0. .1..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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