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 A222139 #10 Mar 15 2018 04:47:22 %S A222139 16,676,28564,1206964,50999956,2154990196,91058563924,3847656513844, %T A222139 162581749707796,6869850581244916,290283793189916884, %U A222139 12265868026121849524,518291141165452870036,21900260661415244606836 %N A222139 Number of n X 3 0..4 arrays with no entry increasing mod 5 by 4 rightwards or downwards, starting with upper left zero. %C A222139 Column 3 of A222144. %H A222139 R. H. Hardin, <a href="/A222139/b222139.txt">Table of n, a(n) for n = 1..210</a> %F A222139 Empirical: a(n) = 45*a(n-1) - 116*a(n-2). %F A222139 Conjectures from _Colin Barker_, Mar 14 2018: (Start) %F A222139 G.f.: 4*x*(4 - 11*x) / (1 - 45*x + 116*x^2). %F A222139 a(n) = (2^(-1-n)*((45-sqrt(1561))^n*(-433+11*sqrt(1561)) + (45+sqrt(1561))^n*(433+11*sqrt(1561)))) / (29*sqrt(1561)). %F A222139 (End) %e A222139 Some solutions for n=3: %e A222139 0 2 4 0 1 1 0 1 4 0 0 2 0 1 3 0 0 0 0 3 4 %e A222139 1 2 0 2 4 1 1 4 0 2 2 2 3 1 1 3 3 1 2 3 4 %e A222139 1 3 1 3 1 2 3 0 1 3 0 2 1 4 1 3 1 1 2 0 1 %Y A222139 Cf. A222144. %K A222139 nonn %O A222139 1,1 %A A222139 _R. H. Hardin_, Feb 09 2013