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 A212403 #14 Oct 29 2012 02:53:43
%S A212403 5,19,74,291,1150,4558,18100,71971,286454,1140954,4547020,18129294,
%T A212403 72309164,288493756,1151300584,4595507491,18346672294,73257044386,
%U A212403 292550538844,1168434892186,4667175448324,18644235526276,74485459541464
%N A212403 Number of binary arrays of length 2*n+1 with no more than n ones in any length 2n subsequence (=50% duty cycle).
%C A212403 Row 2 of A212402.
%H A212403 R. H. Hardin, <a href="/A212403/b212403.txt">Table of n, a(n) for n = 1..210</a>
%F A212403 Recurrence: n*a(n) = 2*(4*n-3)*a(n-1) - 8*(2*n-3)*a(n-2). - _Vaclav Kotesovec_, Oct 19 2012
%F A212403 G.f.: 1/(1-4*x)+1/(2*sqrt(1-4*x)). - _Vaclav Kotesovec_, Oct 21 2012
%F A212403 a(n) = 4^n + C(2*n-1, n). - _Vaclav Kotesovec_, Oct 28 2012
%e A212403 Some solutions for n=3
%e A212403 ..1....0....0....1....0....0....0....1....1....0....1....1....1....0....0....0
%e A212403 ..1....0....0....0....1....0....1....0....0....0....1....0....0....1....1....0
%e A212403 ..1....0....1....1....0....1....1....0....1....0....0....0....0....0....0....1
%e A212403 ..0....1....1....1....0....0....0....0....1....1....0....1....0....0....0....0
%e A212403 ..0....0....1....0....1....1....0....1....0....1....1....0....1....1....0....0
%e A212403 ..0....1....0....0....1....0....1....0....0....0....0....1....1....0....1....0
%e A212403 ..0....1....0....0....0....1....0....1....1....1....0....1....0....0....0....1
%t A212403 Rest[CoefficientList[Series[1/(1-4*x)+1/(2*Sqrt[1-4*x]), {x, 0, 20}], x]] (* _Vaclav Kotesovec_, Oct 21 2012 *)
%t A212403 Table[4^n + Binomial[2*n-1, n],{n,1,20}] (* _Vaclav Kotesovec_, Oct 28 2012 *)
%K A212403 nonn
%O A212403 1,1
%A A212403 _R. H. Hardin_, May 14 2012