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%I #9 May 15 2018 20:43:35
%S 12,72,212,464,860,1432,2212,3232,4524,6120,8052,10352,13052,16184,
%T 19780,23872,28492,33672,39444,45840,52892,60632,69092,78304,88300,
%U 99112,110772,123312,136764,151160,166532,182912,200332,218824,238420,259152
%N Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two consecutive zero elements.
%C Row 4 of A199530.
%H R. H. Hardin, <a href="/A199531/b199531.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = (16/3)*n^3 + 8*n^2 - (4/3)*n.
%F Conjectures from _Colin Barker_, May 15 2018: (Start)
%F G.f.: 4*x*(3 + 6*x - x^2) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F (End)
%e Some solutions for n=5:
%e .-4...-4....4....0...-5....5....2....0...-1...-3....2....1....4...-1....4...-1
%e ..4....5...-4....2....3...-2...-2...-2....0...-2...-2...-3...-1....2...-2....5
%e ..3....1...-2...-5...-3...-1....1....1...-2....2....3....1....0....4....1....1
%e .-3...-2....2....3....5...-2...-1....1....3....3...-3....1...-3...-5...-3...-5
%Y Cf. A199530.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 07 2011
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