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A251258
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T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having a single 1 or two 1s on the same edge
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9
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8, 18, 18, 38, 56, 38, 84, 150, 150, 84, 180, 446, 464, 446, 180, 394, 1232, 1770, 1770, 1232, 394, 850, 3602, 5680, 9130, 5680, 3602, 850, 1852, 10108, 21088, 38332, 38332, 21088, 10108, 1852, 4008, 29272, 69270, 192442, 185620, 192442, 69270, 29272, 4008
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OFFSET
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1,1
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COMMENTS
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Table starts
....8.....18......38.......84........180.........394..........850
...18.....56.....150......446.......1232........3602........10108
...38....150.....464.....1770.......5680.......21088........69270
...84....446....1770.....9130......38332......192442.......836546
..180...1232....5680....38332.....185620.....1215600......6080510
..394...3602...21088...192442....1215600....10753448.....71459218
..850..10108...69270...836546....6080510....71459218....539961360
.1852..29272..252226..4112126...38748690...612889014...6151714502
.4008..82854..842160.18298862..198765264..4229034766..47962536500
.8714.238640.3024532.88585834.1238605998.35355603854.531311887046
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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) +3*a(n-2) -a(n-3)
k=2: a(n) = 3*a(n-1) +4*a(n-2) -14*a(n-3) +3*a(n-4) +3*a(n-5)
k=3: a(n) = a(n-1) +13*a(n-2) -7*a(n-3) -32*a(n-4) +8*a(n-5) +10*a(n-6)
k=4: [order 12]
k=5: [order 17]
k=6: [order 31]
k=7: [order 49]
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..0..0..0....0..0..1..0..0....0..0..1..0..1....1..0..1..1..0
..0..1..0..1..1....1..0..1..0..1....1..0..0..0..0....1..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....0..0..1..0..1....1..0..1..1..0
..1..1..1..0..1....0..1..0..1..0....1..0..1..0..0....1..0..0..0..0
..0..0..0..0..1....0..1..0..1..0....0..0..1..0..1....1..0..1..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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