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