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%I #10 May 25 2018 08:56:37
%S 19,61,151,313,571,949,1471,2161,3043,4141,5479,7081,8971,11173,13711,
%T 16609,19891,23581,27703,32281,37339,42901,48991,55633,62851,70669,
%U 79111,88201,97963,108421,119599,131521,144211,157693,171991,187129,203131
%N Number of arrays of 4 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.
%C Row 4 of A201811.
%H R. H. Hardin, <a href="/A201812/b201812.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*n^3 + 14*n + 1.
%F Conjectures from _Colin Barker_, May 25 2018: (Start)
%F G.f.: x*(19 - 15*x + 21*x^2 - x^3) / (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=21:
%e -6 15 -3 -8 -13 1 13 16 15 -15 3 -21 -6 8 -11 1
%e 9 -12 8 9 9 21 -2 -18 13 9 -7 12 3 20 -18 18
%e 4 -18 16 -17 -13 -14 -13 9 -20 21 -16 19 -11 -7 21 -15
%e -7 15 -21 16 17 -8 2 -7 -8 -15 20 -10 14 -21 8 -4
%Y Cf. A201811.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 05 2011
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