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%I #8 May 25 2018 10:16:29
%S 51,221,631,1401,2651,4501,7071,10481,14851,20301,26951,34921,44331,
%T 55301,67951,82401,98771,117181,137751,160601,185851,213621,244031,
%U 277201,313251,352301,394471,439881,488651,540901,596751,656321,719731
%N Number of arrays of 5 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.
%C Row 5 of A201811.
%H R. H. Hardin, <a href="/A201813/b201813.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 20*n^3 + 30*n + 1.
%F Conjectures from _Colin Barker_, May 25 2018: (Start)
%F G.f.: x*(51 + 17*x + 53*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=17.
%e ..6...13...-8...15..-12...-6...15....0..-13...-5...16....0...17...-4...-3...11
%e ..0...-2....9....3...-2....0..-12....3....0..-17..-17..-16....5....0....0...-8
%e .-8..-12....7...-8....0....6...13...13..-11...12....0...-7...-5...13....7....0
%e ..6....0...-8..-10....1...-3..-16..-10....8...10....3....8..-17..-16....1....2
%e .-4....1....0....0...13....3....0...-6...16....0...-2...15....0....7...-5...-5
%Y Cf. A201811.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 05 2011
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