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 A221525 #8 Aug 06 2018 07:25:17 %S A221525 0,6,94,536,1940,5368,12458,25544,47776,83240,137078,215608,326444, %T A221525 478616,682690,950888,1297208,1737544,2289806,2974040,3812548,4830008, %U A221525 6053594,7513096,9241040,11272808,13646758,16404344,19590236,23252440 %N A221525 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 2 or more. %C A221525 Row 5 of A221524. %H A221525 R. H. Hardin, <a href="/A221525/b221525.txt">Table of n, a(n) for n = 1..210</a> %F A221525 Empirical: a(n) = 1*n^5 - 1*n^4 - 10*n^3 + 38*n^2 - 60*n + 40 for n>2. %F A221525 Conjectures from _Colin Barker_, Aug 06 2018: (Start) %F A221525 G.f.: 2*x^2*(3 + 29*x + 31*x^2 + 7*x^3 - 11*x^4 + 2*x^5 - x^6) / (1 - x)^6. %F A221525 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>8. %F A221525 (End) %e A221525 Some solutions for n=6: %e A221525 ..5....2....6....1....5....4....4....0....4....1....3....6....2....1....2....2 %e A221525 ..2....0....0....5....1....0....2....2....0....4....1....1....6....4....0....6 %e A221525 ..5....4....0....2....6....2....2....5....5....5....1....2....5....1....4....3 %e A221525 ..5....6....6....2....0....2....0....4....0....2....4....0....0....3....2....4 %e A221525 ..3....3....0....0....5....0....6....6....3....6....1....3....4....6....4....0 %Y A221525 Cf. A221524. %K A221525 nonn %O A221525 1,2 %A A221525 _R. H. Hardin_, Jan 19 2013