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 A199705 #17 May 16 2018 06:43:15 %S A199705 6,14,32,52,82,114,156,200,254,310,376,444,522,602,692,784,886,990, %T A199705 1104,1220,1346,1474,1612,1752,1902,2054,2216,2380,2554,2730,2916, %U A199705 3104,3302,3502,3712,3924,4146,4370,4604,4840,5086,5334,5592,5852,6122,6394,6676 %N A199705 Number of -n..n arrays x(0..2) of 3 elements with zero sum and no two neighbors equal. %C A199705 Row 3 of A199704. %H A199705 R. H. Hardin, <a href="/A199705/b199705.txt">Table of n, a(n) for n = 1..200</a> %F A199705 Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4). %F A199705 Conjectures from _Colin Barker_, May 16 2018: (Start) %F A199705 G.f.: 2*x*(3 + x + 2*x^2) / ((1 - x)^3*(1 + x)). %F A199705 a(n) = n + 3*n^2 for n even. %F A199705 a(n) = 2 + n + 3*n^2 for n odd. %F A199705 (End) %e A199705 Some solutions for n=5: %e A199705 ..1...-5....1....1....3...-1...-2....3....1....2....2...-5....3...-3...-3....4 %e A199705 ..3....3...-5....4....0...-4....3...-3...-1...-5....0....5...-2....4....0....1 %e A199705 .-4....2....4...-5...-3....5...-1....0....0....3...-2....0...-1...-1....3...-5 %Y A199705 Cf. A199704. %K A199705 nonn %O A199705 1,1 %A A199705 _R. H. Hardin_, Nov 09 2011