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A200166 Number of -n..n arrays x(0..2) of 3 elements with nonzero sum and with zero through 2 differences all nonzero.

%I A200166 #17 Mar 19 2021 09:58:21
%S A200166 2,34,128,348,726,1326,2180,3352,4874,6810,9192,12084,15518,19558,
%T A200166 24236,29616,35730,42642,50384,59020,68582,79134,90708,103368,117146,
%U A200166 132106,148280,165732,184494,204630,226172,249184,273698,299778,327456,356796
%N A200166 Number of -n..n arrays x(0..2) of 3 elements with nonzero sum and with zero through 2 differences all nonzero.
%C A200166 Row 3 of A200165.
%H A200166 R. H. Hardin, <a href="/A200166/b200166.txt">Table of n, a(n) for n = 1..200</a>
%F A200166 Empirical: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5).
%F A200166 Conjectures from _Colin Barker_, May 17 2018: (Start)
%F A200166 G.f.: 2*x*(1 + 14*x + 15*x^2 + 18*x^3) / ((1 - x)^4*(1 + x)).
%F A200166 a(n) = 11*n - 13*n^2 + 8*n^3 for n even.
%F A200166 a(n) = -4 + 11*n - 13*n^2 + 8*n^3 for n odd.
%F A200166 (End)
%e A200166 Some solutions for n=5:
%e A200166 .-2...-1...-1...-2...-5...-1...-2....2...-2...-4...-1...-3....1...-4....2...-2
%e A200166 ..4....4....4...-4...-1....5....2....4....5....5....3...-1....5...-3....5...-5
%e A200166 .-4...-5....2....4...-2....4...-3....2....2....2...-4...-4...-2...-1....4....5
%Y A200166 Cf. A200165.
%K A200166 nonn
%O A200166 1,1
%A A200166 _R. H. Hardin_, Nov 13 2011