%I #8 Oct 14 2024 15:31:59
%S 1,7,19,151,631,4621,23857,164599,948871,6359617,38944357,258107389,
%T 1636264813,10819063087,70033892299,463844386999,3042796871863,
%U 20218887555601,133836585431269,892623030133681,5947033694372881
%N Number of arrays of n integers in -3..3 with sum zero and equal numbers of elements greater than zero and less than zero.
%H R. H. Hardin, <a href="/A201806/b201806.txt">Table of n, a(n) for n = 1..210</a>
%e Some solutions for n=7:
%e .-3....2....0...-1...-3....3....1....3...-1....3....0...-2....1...-3....0...-3
%e .-3....3...-2...-1....1....1...-1....2...-3....3....1....3....3...-2....0....3
%e .-3....0....3...-2...-1....0...-2...-2....1....1...-2...-3....0....1....2....0
%e ..3...-3...-2....2...-1...-1....3...-2....2...-2....2....3....2....0...-3....0
%e ..3....2....3....1....3....1....0....0....0...-2...-2....2...-1....3...-2....0
%e ..3...-3....1....0....1...-1....1....2...-1...-3....3...-3...-3....2....0...-3
%e ..0...-1...-3....1....0...-3...-2...-3....2....0...-2....0...-2...-1....3....3
%Y Column 3 of A201811.
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 05 2011