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 A212407 #18 May 11 2019 02:21:24
%S A212407 34,166,747,3179,13185,54042,220054,892387,3609005,14567294,58714842,
%T A212407 236397086,950965002,3822869204,15359318444,61681353571,247609729669,
%U A212407 993662549686,3986465243314,15989373858826,64118439206974
%N A212407 Number of binary arrays of length 2*n+5 with no more than n ones in any length 2n subsequence (=50% duty cycle).
%H A212407 R. H. Hardin, <a href="/A212407/b212407.txt">Table of n, a(n) for n = 1..210</a>
%F A212407 Empirical (for n>=5): n*(181*n^2 - 792*n + 581)*a(n) = 2*(724*n^3 - 3711*n^2 + 4112*n + 210)*a(n-1) - 8*(2*n-7)*(181*n^2 - 430*n - 30)*a(n-2). - _Vaclav Kotesovec_, Nov 20 2012
%F A212407 Empirical (for n>=3): a(n) = 4^(n+2) - 2*(181*n^2 - 264*n - 6) * C(2*n - 5, n - 3) / (n*(n-1)). - _Vaclav Kotesovec_, Nov 20 2012
%e A212407 Some solutions for n=3:
%e A212407 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 1
%e A212407 0 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0
%e A212407 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0
%e A212407 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0
%e A212407 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0
%e A212407 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
%e A212407 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 0
%e A212407 0 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0
%e A212407 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1
%e A212407 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 0
%e A212407 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1
%p A212407 #verified first terms (holds for all n<=210).
%p A212407 with(gfun): A212407:= rectoproc({a(3)=747, a(4)=3179, n*(181*n^2-792*n+581)*a(n) = 2*(724*n^3-3711*n^2+4112*n+210)*a(n-1) - 8*(2*n-7)*(181*n^2-430*n-30)*a(n-2)},a(n),remember): 34,166,seq(A212407(n),n=3..20); A212407(210); # _Vaclav Kotesovec_, Nov 20 2012
%Y A212407 Row 6 of A212402.
%K A212407 nonn
%O A212407 1,1
%A A212407 _R. H. Hardin_, May 14 2012