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%I #16 Oct 29 2012 07:07:59
%S 1,7,34,151,646,2710,11236,46231,189214,771442,3136156,12720982,
%T 51507964,208260556,841065544,3393346711,13679459854,55106773786,
%U 221860011244,892741834546,3590659699444,14436037598836,58018598086264
%N Number of binary arrays of length 2*n+1 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).
%C Row 2 of A213118.
%H R. H. Hardin, <a href="/A213119/b213119.txt">Table of n, a(n) for n = 1..210</a>
%F Recurrence: n*a(n) = 2*(4*n-3)*a(n-1) - 8*(2*n-3)*a(n-2). - _Vaclav Kotesovec_, Oct 19 2012
%F G.f.: 1/(1-4*x)-3/(2*sqrt(1-4*x)). - _Vaclav Kotesovec_, Oct 21 2012
%F a(n) = 4^n - 3*C(2*n-1,n). - _Vaclav Kotesovec_, Oct 29 2012
%e Some solutions for n=3
%e ..0....0....1....1....0....1....1....0....1....1....0....0....0....0....0....0
%e ..0....1....0....0....0....0....0....0....0....0....1....0....0....0....0....0
%e ..0....0....0....0....0....0....0....1....0....0....1....1....0....0....1....0
%e ..1....0....0....0....0....0....0....0....1....0....0....1....1....1....0....0
%e ..0....1....1....0....0....0....0....0....0....1....0....0....1....0....0....0
%e ..1....0....0....1....1....0....1....0....0....0....0....0....0....0....0....1
%e ..0....0....0....0....1....1....1....0....0....1....0....0....0....0....1....0
%t Table[4^n-3*Binomial[2*n-1,n],{n,1,20}] (* _Vaclav Kotesovec_, Oct 29 2012 *)
%K nonn
%O 1,2
%A _R. H. Hardin_, Jun 05 2012
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