This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A213119 #16 Oct 29 2012 07:07:59
%S A213119 1,7,34,151,646,2710,11236,46231,189214,771442,3136156,12720982,
%T A213119 51507964,208260556,841065544,3393346711,13679459854,55106773786,
%U A213119 221860011244,892741834546,3590659699444,14436037598836,58018598086264
%N A213119 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 A213119 Row 2 of A213118.
%H A213119 R. H. Hardin, <a href="/A213119/b213119.txt">Table of n, a(n) for n = 1..210</a>
%F A213119 Recurrence: n*a(n) = 2*(4*n-3)*a(n-1) - 8*(2*n-3)*a(n-2). - _Vaclav Kotesovec_, Oct 19 2012
%F A213119 G.f.: 1/(1-4*x)-3/(2*sqrt(1-4*x)). - _Vaclav Kotesovec_, Oct 21 2012
%F A213119 a(n) = 4^n - 3*C(2*n-1,n). - _Vaclav Kotesovec_, Oct 29 2012
%e A213119 Some solutions for n=3
%e A213119 ..0....0....1....1....0....1....1....0....1....1....0....0....0....0....0....0
%e A213119 ..0....1....0....0....0....0....0....0....0....0....1....0....0....0....0....0
%e A213119 ..0....0....0....0....0....0....0....1....0....0....1....1....0....0....1....0
%e A213119 ..1....0....0....0....0....0....0....0....1....0....0....1....1....1....0....0
%e A213119 ..0....1....1....0....0....0....0....0....0....1....0....0....1....0....0....0
%e A213119 ..1....0....0....1....1....0....1....0....0....0....0....0....0....0....0....1
%e A213119 ..0....0....0....0....1....1....1....0....0....1....0....0....0....0....1....0
%t A213119 Table[4^n-3*Binomial[2*n-1,n],{n,1,20}] (* _Vaclav Kotesovec_, Oct 29 2012 *)
%K A213119 nonn
%O A213119 1,2
%A A213119 _R. H. Hardin_, Jun 05 2012