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 A303714 #8 May 17 2023 12:14:53 %S A303714 3,3,5,8,14,24,40,68,116,196,332,564,956,1620,2748,4660,7900,13396, %T A303714 22716,38516,65308,110740,187772,318388,539868,915412,1552188,2631924, %U A303714 4462748,7567124,12830972,21756468,36890716,62552660,106065596,179847028 %N A303714 Number of n X 3 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero. %C A303714 Column 3 of A303719. %H A303714 R. H. Hardin, <a href="/A303714/b303714.txt">Table of n, a(n) for n = 1..210</a> %F A303714 Empirical: a(n) = a(n-1) +2*a(n-3) for n>4. %F A303714 Empirical g.f.: 3*x-x^2*(3+2*x+3*x^2)/(-1+x+2*x^3). - _R. J. Mathar_, Apr 30 2018 %e A303714 Some solutions for n=5 %e A303714 ..0..0..0. .0..1..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0 %e A303714 ..0..0..0. .0..0..0. .0..0..0. .1..0..0. .0..0..0. .0..0..1. .0..0..0 %e A303714 ..1..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..1 %e A303714 ..0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0 %e A303714 ..0..0..0. .0..1..0. .0..0..0. .0..0..0. .0..1..0. .0..1..0. .0..0..0 %Y A303714 Cf. A303719. %K A303714 nonn %O A303714 1,1 %A A303714 _R. H. Hardin_, Apr 29 2018