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 A221677 #10 Oct 19 2017 06:14:13 %S A221677 0,2,5,14,40,113,320,906,2565,7262,20560,58209,164800,466578,1320965, %T A221677 3739886,10588280,29977297,84871040,240284954,680289285,1926019518, %U A221677 5452902560,15438133441,43708091520,123745352482,350345021445 %N A221677 Number of 0..2 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0. %C A221677 Column 2 of A221683. %H A221677 R. H. Hardin, <a href="/A221677/b221677.txt">Table of n, a(n) for n = 1..210</a> %F A221677 Empirical: a(n) = 2*a(n-1) +2*a(n-2) +a(n-3). %F A221677 Empirical g.f.: x^2*(2 + x) / (1 - 2*x - 2*x^2 - x^3). - _Colin Barker_, Oct 19 2017 %e A221677 Some solutions for n=6 %e A221677 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0 %e A221677 ..1....1....1....1....1....1....1....0....1....0....1....1....1....0....0....1 %e A221677 ..2....1....0....0....1....0....2....2....2....1....2....1....2....2....1....0 %e A221677 ..0....1....0....0....1....0....2....2....0....1....0....2....1....2....0....0 %e A221677 ..1....0....2....0....2....1....2....0....0....0....0....1....2....1....1....1 %e A221677 ..0....1....2....1....2....1....1....0....1....1....0....2....1....0....0....0 %K A221677 nonn %O A221677 1,2 %A A221677 _R. H. Hardin_, Jan 22 2013