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A213120
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Number of binary arrays of length 2*n+2 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).
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1
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1, 10, 54, 252, 1110, 4748, 19964, 83024, 342678, 1406748, 5751636, 23443240, 95319484, 386805112, 1567130168, 6340730552, 25626393878, 103472018492, 417449893988, 1682982404072, 6780908053268, 27306234108392, 109907864408648
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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Recurrence: n*(5*n-13)*a(n) = 2*(20*n^2-67*n+40)*a(n-1) - 8*(2*n-5)*(5*n-8) * a(n-2). - Vaclav Kotesovec, Oct 19 2012
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EXAMPLE
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Some solutions for n=3
..0....0....0....0....1....1....0....0....0....0....0....0....0....1....0....1
..0....1....0....0....0....0....0....1....0....0....0....0....1....1....0....0
..0....1....1....0....1....1....0....0....0....0....0....1....0....0....1....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....1....1....0....0....0....1....0....0....0....1
..1....0....1....0....0....0....0....0....0....1....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....1....1....0....0....1....0....0....1
..0....1....0....0....0....1....1....0....0....0....1....0....1....1....1....0
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MATHEMATICA
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Table[2^(2*n+1)-(15*n-8)*Binomial[2*n-2, n-1]/n, {n, 1, 20}] (* Vaclav Kotesovec, Oct 29 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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