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%I #10 Oct 29 2012 02:53:32
%S 13,57,236,959,3872,15586,62632,251419,1008536,4043582,16206152,
%T 64933782,260114976,1041797124,4171943056,16704821779,66880877896,
%U 267747443494,1071808583176,4290243456514,17172082337536,68729504287324
%N Number of binary arrays of length 2*n+3 with no more than n ones in any length 2n subsequence (=50% duty cycle)
%C Row 4 of A212402
%H R. H. Hardin, <a href="/A212405/b212405.txt">Table of n, a(n) for n = 1..210</a>
%F 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
%F a(n) = 2^(2*n+2) - (3*n+1)/n * C(2*n-2,n-1), for n>1. - _Vaclav Kotesovec_, Oct 28 2012
%e Some solutions for n=3
%e ..1....0....0....1....0....0....1....1....1....0....1....0....1....0....0....0
%e ..0....0....0....1....0....0....0....0....0....0....1....0....0....0....1....1
%e ..1....1....0....1....1....0....1....0....1....1....1....0....0....1....0....0
%e ..1....0....0....0....0....0....0....1....0....0....0....0....0....0....1....1
%e ..0....1....0....0....1....0....0....0....0....1....0....0....1....0....1....0
%e ..0....0....1....0....0....1....1....0....1....1....0....0....0....0....0....1
%e ..0....0....1....0....1....0....1....0....0....0....1....0....0....0....0....0
%e ..1....0....1....1....0....1....0....1....0....0....0....1....1....0....1....0
%e ..1....1....0....1....0....1....1....1....1....1....1....0....0....0....0....0
%t 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 *)
%K nonn
%O 1,1
%A _R. H. Hardin_ May 14 2012
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