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%I #5 Mar 31 2012 12:36:56
%S 6,21,104,444,1614,5036,13934,34847,80258,172405,349182,672246,
%T 1238648,2196082,3763716,6258579,10130162,16003183,24731962,37466168,
%U 55732478,81531582,117456262,166829725,233871176,323887385,443498894,600898968
%N Number of arrays of 10 nondecreasing integers in -n..n with sum zero and equal numbers greater than zero and less than zero
%C Row 5 of A203291
%H R. H. Hardin, <a href="/A203295/b203295.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) -2*a(n-5) +5*a(n-6) +a(n-7) +a(n-8) -3*a(n-9) -7*a(n-10) +2*a(n-11) +2*a(n-12) +4*a(n-13) +2*a(n-14) +2*a(n-15) -7*a(n-16) -3*a(n-17) +a(n-18) +a(n-19) +5*a(n-20) -2*a(n-21) +a(n-22) -3*a(n-23) -a(n-24) +3*a(n-25) -a(n-26)
%e Some solutions for n=3
%e .-2...-3...-3...-3...-3...-3...-3...-2...-3...-2...-3...-3...-3...-3...-3...-2
%e .-2...-3...-3...-2...-2...-2...-3...-2...-3...-1...-3...-3...-1....0...-3...-2
%e .-2....0...-3...-1...-2...-2...-2...-2...-3...-1...-3...-3...-1....0...-1...-2
%e .-2....0...-1....0...-1...-1...-2....0...-3...-1...-1....0....0....0...-1...-2
%e .-2....0...-1....0...-1....0....0....0...-1...-1...-1....0....0....0....0....0
%e ..1....0....1....0....1....0....0....0....1....1....2....0....0....0....0....0
%e ..2....0....1....0....1....2....2....0....3....1....2....0....0....0....1....1
%e ..2....0....3....2....2....2....2....1....3....1....2....3....1....0....1....2
%e ..2....3....3....2....2....2....3....2....3....1....2....3....2....0....3....2
%e ..3....3....3....2....3....2....3....3....3....2....3....3....2....3....3....3
%K nonn
%O 1,1
%A _R. H. Hardin_ Dec 31 2011
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