%I #8 May 15 2018 20:43:48
%S 80,1414,8342,30484,84852,197962,407946,766664,1341816,2219054,
%T 3504094,5324828,7833436,11208498,15657106,21416976,28758560,37987158,
%U 49445030,63513508,80615108,101215642,125826330,155005912,189362760,229556990
%N Number of -n..n arrays x(0..5) of 6 elements with zero sum and no two consecutive zero elements.
%C Row 6 of A199530.
%H R. H. Hardin, <a href="/A199533/b199533.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = (88/5)*n^5 + 44*n^4 + (58/3)*n^3 - 3*n^2 + (31/15)*n.
%F Conjectures from _Colin Barker_, May 15 2018: (Start)
%F G.f.: 2*x*(40 + 467*x + 529*x^2 + 21*x^3 - x^4) / (1 - x)^6.
%F 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>6.
%F (End)
%e Some solutions for n=5:
%e ..1....5...-4....0....5...-3...-1...-3....5....5...-5....0...-3....3....3....4
%e ..3....1....2....5....5...-1....2...-4....4...-3...-2...-3....4....3....1...-1
%e ..3...-5...-3...-3....1...-1....5....1...-5....3....3....4...-3...-1....3....1
%e .-1....0....4...-2...-3...-4...-3...-2....0....0....5....0...-1...-5....0....0
%e .-2...-3....4...-4...-3....4...-2....3...-5...-5....2...-3...-1....2...-2...-2
%e .-4....2...-3....4...-5....5...-1....5....1....0...-3....2....4...-2...-5...-2
%Y Cf. A199530.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 07 2011