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A212405
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Number of binary arrays of length 2*n+3 with no more than n ones in any length 2n subsequence (=50% duty cycle)
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1
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13, 57, 236, 959, 3872, 15586, 62632, 251419, 1008536, 4043582, 16206152, 64933782, 260114976, 1041797124, 4171943056, 16704821779, 66880877896, 267747443494, 1071808583176, 4290243456514, 17172082337536, 68729504287324
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Recurrence (for n>3): n^2*a(n) = 2*(4*n^2-3*n-5)*a(n-1) - 8*(n+1)*(2*n-5)*a(n-2). - Vaclav Kotesovec, Oct 19 2012
a(n) = 2^(2*n+2) - (3*n+1)/n * C(2*n-2,n-1), for n>1. - Vaclav Kotesovec, Oct 28 2012
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EXAMPLE
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Some solutions for n=3
..1....0....0....1....0....0....1....1....1....0....1....0....1....0....0....0
..0....0....0....1....0....0....0....0....0....0....1....0....0....0....1....1
..1....1....0....1....1....0....1....0....1....1....1....0....0....1....0....0
..1....0....0....0....0....0....0....1....0....0....0....0....0....0....1....1
..0....1....0....0....1....0....0....0....0....1....0....0....1....0....1....0
..0....0....1....0....0....1....1....0....1....1....0....0....0....0....0....1
..0....0....1....0....1....0....1....0....0....0....1....0....0....0....0....0
..1....0....1....1....0....1....0....1....0....0....0....1....1....0....1....0
..1....1....0....1....0....1....1....1....1....1....1....0....0....0....0....0
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MATHEMATICA
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Flatten[{13, Table[2^(2*n+2)-(3*n+1)/n*Binomial[2*n-2, n-1], {n, 2, 20}]}] (* Vaclav Kotesovec, Oct 28 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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