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 A194772 #10 May 05 2018 08:24:00 %S A194772 7,17,41,95,219,493,1101,2427,5311,11529,24881,53399,114083,242725, %T A194772 514581,1087411,2291335,4815681,10097401,21126863,44117867,91963997, %U A194772 191384541,397682155,825190479,1710033273,3539371201,7317351687 %N A194772 Number of lower triangles of an (n+2) X (n+2) 0..2 array with new values introduced in row major order 0..2 and no element unequal to more than one horizontal or vertical neighbor. %C A194772 Column 2 of A194778. %H A194772 R. H. Hardin, <a href="/A194772/b194772.txt">Table of n, a(n) for n = 1..34</a> %F A194772 Empirical: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +4*a(n-5). %F A194772 Conjectures from _Colin Barker_, May 05 2018: (Start) %F A194772 G.f.: x*(7 - 4*x - 17*x^2 + 4*x^3 + 12*x^4) / ((1 - x)*(1 + x)^2*(1 - 2*x)^2). %F A194772 a(n) = (-3*n + 2^(n+3)*(3*n+8) + 17) / 27 for n even. %F A194772 a(n) = (3*n + 2^(n+3)*(3*n+8) + 10) / 27 for n odd. %F A194772 (End) %e A194772 All solutions for 3 X 3 including a 2. %e A194772 ..0 %e A194772 ..1.1 %e A194772 ..1.1.2 %Y A194772 Cf. A194778. %K A194772 nonn %O A194772 1,1 %A A194772 _R. H. Hardin_, Sep 02 2011