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 A221567 #9 Jun 02 2025 08:21:30 %S A221567 0,5,9,25,57,141,345,853,2097,5149,12633,31013,76161,187053,459369, %T A221567 1128053,2770065,6802301,16704249,41020357,100732833,247366989, %U A221567 607452297,1491704341,3663139761,8995478557,22089965337,54245756261,133209897153 %N A221567 Number of 0..2 arrays of length n with each element differing from at least one neighbor by something other than 1. %C A221567 Column 2 of A221573 %H A221567 R. H. Hardin, <a href="/A221567/b221567.txt">Table of n, a(n) for n = 1..210</a> %F A221567 Empirical: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-4). %F A221567 Empirical g.f.: -x^2*(5-6*x+8*x^2) / ( -1+3*x-2*x^2+4*x^4 ). - _R. J. Mathar_, Jun 06 2013 %e A221567 Some solutions for n=6 %e A221567 ..2....1....2....0....0....1....2....0....0....0....0....2....0....2....0....1 %e A221567 ..0....1....2....0....0....1....0....2....2....0....0....0....0....2....0....1 %e A221567 ..0....1....1....2....2....0....0....2....2....2....2....1....2....1....0....2 %e A221567 ..0....0....1....2....0....0....0....0....0....0....2....1....2....1....2....2 %e A221567 ..2....0....2....2....2....1....1....2....0....0....1....2....2....2....0....0 %e A221567 ..0....0....2....2....2....1....1....2....2....2....1....0....0....0....0....2 %K A221567 nonn %O A221567 1,2 %A A221567 _R. H. Hardin_ Jan 20 2013