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A251292
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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 or main diagonally
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9
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9, 22, 22, 52, 71, 52, 125, 219, 219, 125, 297, 701, 822, 701, 297, 710, 2193, 3390, 3390, 2193, 710, 1691, 6980, 12954, 18924, 12954, 6980, 1691, 4036, 21966, 52474, 94706, 94706, 52474, 21966, 4036, 9621, 69681, 202882, 518711, 577942, 518711, 202882
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OFFSET
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1,1
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COMMENTS
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Table starts
.....9.....22.......52.......125........297..........710..........1691
....22.....71......219.......701.......2193.........6980.........21966
....52....219......822......3390......12954........52474........202882
...125....701.....3390.....18924......94706.......518711.......2645966
...297...2193....12954.....94706.....577942......4109933......25654154
...710...6980....52474....518711....4109933.....39473392.....322933003
..1691..21966...202882...2645966...25654154....322933003....3232216177
..4036..69681...813336..14292754..178853600...3029148345...39571705178
..9621.219860..3168621..73763850.1134888362..25329125380..405845538185
.22951.696284.12623928.394839392.7800498387.233446638426.4863503527792
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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) +2*a(n-2) -3*a(n-3) +a(n-4)
k=2: a(n) = 2*a(n-1) +7*a(n-2) -9*a(n-3) -7*a(n-4) +7*a(n-5) for n>6
k=3: [order 11]
k=4: [order 19]
k=5: [order 33] for n>34
k=6: [order 58] for n>59
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..0..0..0....1..1..1..1..1....0..1..0..0..0....1..0..0..0..0
..1..1..0..1..1....0..0..0..0..0....0..0..1..0..1....0..1..1..1..1
..0..0..0..0..0....1..0..1..1..0....1..0..1..0..1....0..0..0..0..0
..0..1..0..1..1....1..0..0..0..1....1..0..0..0..1....1..1..0..1..0
..0..1..0..0..0....0..1..1..0..0....1..0..1..0..0....0..0..0..0..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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