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 A221574 #8 Aug 08 2018 15:19:04 %S A221574 2,9,26,59,114,197,314,471,674,929,1242,1619,2066,2589,3194,3887,4674, %T A221574 5561,6554,7659,8882,10229,11706,13319,15074,16977,19034,21251,23634, %U A221574 26189,28922,31839,34946,38249,41754,45467,49394,53541,57914,62519,67362 %N A221574 Number of 0..n arrays of length 3 with each element differing from at least one neighbor by something other than 1. %C A221574 Row 3 of A221573. %H A221574 R. H. Hardin, <a href="/A221574/b221574.txt">Table of n, a(n) for n = 1..210</a> %F A221574 Empirical: a(n) = 1*n^3 - 1*n^2 + 3*n - 1. %F A221574 Conjectures from _Colin Barker_, Aug 08 2018: (Start) %F A221574 G.f.: x*(2 + x)*(1 + x^2) / (1 - x)^4. %F A221574 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. %F A221574 (End) %e A221574 Some solutions for n=6: %e A221574 ..1....0....5....2....5....0....6....6....6....0....6....0....1....1....6....5 %e A221574 ..6....5....1....4....3....5....4....6....4....4....1....4....1....3....2....1 %e A221574 ..4....5....1....4....1....2....0....4....2....0....6....4....3....0....5....5 %Y A221574 Cf. A221573. %K A221574 nonn %O A221574 1,1 %A A221574 _R. H. Hardin_, Jan 20 2013