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 A202195 #13 Mar 03 2018 05:35:45 %S A202195 108,240,450,756,1176,1728,2430,3300,4356,5616,7098,8820,10800,13056, %T A202195 15606,18468,21660,25200,29106,33396,38088,43200,48750,54756,61236, %U A202195 68208,75690,83700,92256,101376,111078,121380,132300,143856,156066,168948 %N A202195 Number of (n+2) X 3 binary arrays avoiding patterns 001 and 101 in rows and columns. %C A202195 Column 1 of A202202. %H A202195 R. H. Hardin, <a href="/A202195/b202195.txt">Table of n, a(n) for n = 1..210</a> %F A202195 Empirical: a(n) = 3*(n+3)*(n+2)^2 = 3*A011379(n+2). %F A202195 Conjectures from _Colin Barker_, Mar 03 2018: (Start) %F A202195 G.f.: 6*x*(18 - 32*x + 23*x^2 - 6*x^3) / (1 - x)^4. %F A202195 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4. %F A202195 (End) %e A202195 Some solutions for n=10: %e A202195 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 1 %e A202195 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 %e A202195 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 %e A202195 1 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 %e A202195 1 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 1 1 1 1 %e A202195 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 %e A202195 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 %e A202195 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 %e A202195 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 %e A202195 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 %e A202195 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 %e A202195 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 %Y A202195 Cf. A202202. %K A202195 nonn %O A202195 1,1 %A A202195 _R. H. Hardin_, Dec 14 2011