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 A213123 #18 May 11 2019 02:21:38
%S A213123 1,26,212,1198,5842,26630,116992,502492,2126238,8903350,36998056,
%T A213123 152862180,628749892,2576996188,10531805664,42940549576,174734720374,
%U A213123 709858318486,2879728611544,11668224303796,47228199967804
%N A213123 Number of binary arrays of length 2*n+5 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).
%H A213123 R. H. Hardin, <a href="/A213123/b213123.txt">Table of n, a(n) for n = 1..210</a>
%F A213123 Empirical (for n>=5): n*(33*n^2 - 213*n + 340)*a(n) = 2*(132*n^3 - 951*n^2 + 2029*n - 1120)*a(n-1) - 8*(2*n-7)*(33*n^2 - 147*n + 160)*a(n-2). - _Vaclav Kotesovec_, Nov 20 2012
%F A213123 Empirical (for n>=3): a(n) = 4^(n+2) - 42*(33*n^2 - 71*n + 32) * C(2*n - 5, n - 3) / ((n-1)*n). - _Vaclav Kotesovec_, Nov 20 2012
%e A213123 Some solutions for n=3:
%e A213123 0 1 1 0 0 1 1 0 0 0 1 0 1 0 1 0
%e A213123 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0
%e A213123 0 1 0 1 1 0 0 0 0 1 1 0 0 0 0 0
%e A213123 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0
%e A213123 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
%e A213123 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
%e A213123 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e A213123 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0
%e A213123 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0
%e A213123 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1
%e A213123 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0
%p A213123 #verified first terms (holds for all n<=210).
%p A213123 with(gfun): A213123:= rectoproc({a(3)=212, a(4)=1198, n*(33*n^2-213*n+340)*a(n) = 2*(132*n^3-951*n^2+2029*n-1120)*a(n-1) - 8*(2*n-7)*(33*n^2-147*n+160)*a(n-2)},a(n),remember): 1,26,seq(A213123(n),n=3..20); A213123(210); # _Vaclav Kotesovec_, Nov 20 2012
%Y A213123 Row 6 of A213118.
%K A213123 nonn
%O A213123 1,2
%A A213123 _R. H. Hardin_, Jun 05 2012