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A188860
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Number of n X n binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.
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2
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1, 2, 7, 26, 95, 340, 1193, 4116, 14001, 47064, 156629, 516844, 1693073, 5511218, 17841247, 57477542, 184377699, 589195584, 1876395357, 5957318820, 18861068265, 59563612974, 187668462027, 590039959434, 1851508693479, 5799494052414, 18135645594003
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (3*x^2-3*x+1-x*sqrt(1-3*x^2-2*x))/(1-3*x)^2. - Alois P. Heinz, Mar 30 2017
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EXAMPLE
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Some solutions for 3X3
..1..1..1....0..0..0....1..1..1....1..1..1....1..1..0....1..1..1....1..1..1
..1..1..1....0..0..0....1..1..1....1..0..0....0..0..0....1..1..1....1..1..1
..1..1..0....0..0..0....1..0..0....0..0..0....0..0..0....1..0..1....0..0..0
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MAPLE
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a:= proc(n) option remember; `if`(n<3, (2*n-1)*n+1,
((10*n^2-49*n+33)*a(n-1)-(6*n^2-9*n-33)*a(n-2)
-(9*(n-3))*(2*n-7)*a(n-3))/((n-1)*(2*n-9)))
end:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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