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%I #9 May 25 2018 10:33:27
%S 141,1001,4621,15681,42821,99961,207621,394241,697501,1165641,1858781,
%T 2850241,4227861,6095321,8573461,11801601,15938861,21165481,27684141,
%U 35721281,45528421,57383481,71592101,88488961,108439101,131839241
%N Number of arrays of 6 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.
%C Row 6 of A201811.
%H R. H. Hardin, <a href="/A201814/b201814.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 11*n^5 + 65*n^3 + 64*n + 1.
%F Conjectures from _Colin Barker_, May 25 2018: (Start)
%F G.f.: x*(141 + 155*x + 730*x^2 + 150*x^3 + 145*x^4 - x^5) / (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=6:
%e ..6....4....2...-5...-6....6....2...-2...-4...-4...-4....0....4...-4....5...-4
%e .-5....1....6...-1....2....5...-4...-4...-1....1...-3....5...-1....1...-3...-1
%e .-4...-4...-5....3....5....1...-2....0....3...-1....4...-4....3...-4...-5....4
%e ..1...-2...-4....5...-1...-5....2....2...-6....6....1....0...-4...-1....5....1
%e .-1....4...-3...-4...-6...-5...-1....0....6....1...-3...-2...-6....2....2...-4
%e ..3...-3....4....2....6...-2....3....4....2...-3....5....1....4....6...-4....4
%Y Cf. A201811.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 05 2011
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