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 A213122 #9 Jun 02 2025 08:01:00 %S A213122 1,19,136,714,3354,14946,64664,274676,1152494,4793874,19813536, %T A213122 81495084,333932596,1364199604,5559496912,22610923448,91805888342, %U A213122 372224952818,1507347830672,6097720950428,24644919356012,99527343620348 %N A213122 Number of binary arrays of length 2*n+4 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle). %C A213122 Row 5 of A213118 %H A213122 R. H. Hardin, <a href="/A213122/b213122.txt">Table of n, a(n) for n = 1..210</a> %F A213122 Empirical: 3*n*(77*n-237)*a(n) = 2*(924*n^2-3545*n+2311)*a(n-1) - 8*(462*n^2-2131*n+2347)*a(n-2) - 128*(2*n-9)*a(n-3). - _Vaclav Kotesovec_, Oct 19 2012 %e A213122 Some solutions for n=3 %e A213122 ..0....0....0....0....0....0....0....0....1....1....1....0....0....0....1....1 %e A213122 ..1....0....1....0....0....0....1....0....0....0....0....0....0....1....0....0 %e A213122 ..0....0....0....0....0....0....0....1....0....1....0....0....1....0....1....0 %e A213122 ..0....0....0....0....0....0....0....0....1....0....0....1....0....0....0....0 %e A213122 ..1....0....0....0....1....0....1....0....0....0....0....0....0....0....0....0 %e A213122 ..0....1....0....0....1....0....0....1....0....0....0....0....0....0....0....0 %e A213122 ..0....0....0....1....0....1....0....0....0....1....0....0....0....1....0....0 %e A213122 ..1....0....0....1....0....0....0....0....0....0....1....1....1....0....1....1 %e A213122 ..0....0....1....0....0....1....0....1....0....1....0....0....0....0....0....0 %e A213122 ..0....1....0....0....0....0....1....0....1....0....1....0....1....1....0....0 %K A213122 nonn %O A213122 1,2 %A A213122 _R. H. Hardin_ Jun 05 2012