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 A212408 #18 May 11 2019 02:21:31
%S A212408 55,285,1314,5769,24322,100736,413220,1685039,6844362,27724036,
%T A212408 112072540,452348578,1823583124,7344493104,29556979016,118871913787,
%U A212408 477820811258,1919788147772,7710323488748,30956089143902,124248950086268
%N A212408 Number of binary arrays of length 2*n+6 with no more than n ones in any length 2n subsequence (=50% duty cycle).
%H A212408 R. H. Hardin, <a href="/A212408/b212408.txt">Table of n, a(n) for n = 1..210</a>
%F A212408 Empirical (for n>=5): n*(955*n^3 - 8481*n^2 + 21998*n - 14262)*a(n) = 2*(3820*n^4 - 36789*n^3 + 110342*n^2 - 99213*n - 1890)*a(n-1) - 8*(2*n-9)*(955*n^3 - 5616*n^2 + 7901*n + 210)*a(n-2). - _Vaclav Kotesovec_, Nov 20 2012
%F A212408 Empirical (for n>=4): a(n) = 2^(2*n+5) - 4*(955*n^3 - 3782*n^2 + 3475*n + 30) * C(2*n-7, n-4) / ((n-2)*(n-1)*n). - _Vaclav Kotesovec_, Nov 20 2012
%e A212408 Some solutions for n=3:
%e A212408 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1
%e A212408 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0
%e A212408 0 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0
%e A212408 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1
%e A212408 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1
%e A212408 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
%e A212408 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 0
%e A212408 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0
%e A212408 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0
%e A212408 1 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0
%e A212408 0 1 0 0 0 0 0 0 1 1 0 0 1 0 1 0
%e A212408 1 0 1 1 1 0 1 0 1 1 1 1 0 0 0 0
%p A212408 #verified first terms (holds for all n<=210).
%p A212408 with(gfun): A212408:= rectoproc({a(3)=1314, a(4)=5769, n*(955*n^3-8481*n^2+21998*n-14262)*a(n) = 2*(3820*n^4-36789*n^3+110342*n^2-99213*n-1890)*a(n-1) - 8*(2*n-9)*(955*n^3-5616*n^2+7901*n+210)*a(n-2)},a(n),remember): 55,285,seq(A212408(n),n=3..20); A212408(210); # _Vaclav Kotesovec_, Nov 20 2012
%Y A212408 Row 7 of A212402.
%K A212408 nonn
%O A212408 1,1
%A A212408 _R. H. Hardin_, May 14 2012