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 A208044 #11 Mar 07 2018 02:31:01 %S A208044 2,8,44,244,1356,7540,41932,233204,1296972,7213172,40116428,223109620, %T A208044 1240835916,6900974452,38380133836,213453141236,1187130917964, %U A208044 6602291295860,36718991727308,204214611724276,1135750348251468 %N A208044 Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors). %C A208044 Column 3 of A208050. %H A208044 R. H. Hardin, <a href="/A208044/b208044.txt">Table of n, a(n) for n = 1..210</a> %F A208044 Empirical: a(n) = 7*a(n-1) - 8*a(n-2) for n>3. %F A208044 Conjectures from _Colin Barker_, Mar 06 2018: (Start) %F A208044 G.f.: 2*x*(1 - x)*(1 - 2*x) / (1 - 7*x + 8*x^2). %F A208044 a(n) = (2^(-5-n)*((7-sqrt(17))^n*(-13+5*sqrt(17)) + (7+sqrt(17))^n*(13+5*sqrt(17)))) / sqrt(17) for n>1. %F A208044 (End) %e A208044 Some solutions for n=4: %e A208044 0 1 0 0 1 0 0 1 2 0 1 0 0 1 2 0 1 0 0 1 2 %e A208044 2 3 2 2 3 1 2 0 3 2 3 1 2 3 0 2 3 1 2 3 0 %e A208044 1 0 1 1 2 0 3 1 2 0 2 0 0 1 3 0 2 3 0 1 2 %e A208044 2 3 2 3 1 2 0 3 1 1 3 1 2 0 1 3 1 2 2 3 1 %Y A208044 Cf. A208050. %K A208044 nonn %O A208044 1,1 %A A208044 _R. H. Hardin_, Feb 22 2012