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%I #5 Mar 31 2012 12:36:56
%S 7,54,310,1380,5036,15798,43958,111053,259023,565010,1164062,2283094,
%T 4289830,7762060,13582916,23070101,38147395,61569710,97213302,
%U 150446614,228597390,341536652,502400112,728473703,1042269641,1472826974
%N Number of arrays of 2n nondecreasing integers in -6..6 with sum zero and equal numbers greater than zero and less than zero
%C Column 6 of A203291
%H R. H. Hardin, <a href="/A203289/b203289.txt">Table of n, a(n) for n = 1..121</a>
%F Empirical: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -3*a(n-5) +7*a(n-6) -4*a(n-7) -4*a(n-9) -4*a(n-10) +9*a(n-11) +2*a(n-13) -2*a(n-14) -9*a(n-16) +4*a(n-17) +4*a(n-18) +4*a(n-20) -7*a(n-21) +3*a(n-22) -4*a(n-23) +2*a(n-24) +4*a(n-25) -4*a(n-26) +a(n-27)
%e Some solutions for n=3
%e .-5...-6...-3...-3...-2...-5...-4...-5...-6...-3...-4...-4...-6...-2...-3...-6
%e .-5...-2...-3...-3...-2...-4...-4...-4...-6...-3...-4...-4...-4...-2...-2...-5
%e .-2...-1....0...-1...-2...-3...-3...-3...-2...-2...-2...-1...-4....0...-2...-4
%e ..1....1....0....1....1....1....1....3....4....1....2....1....3....0....1....5
%e ..5....2....2....1....1....5....5....3....5....2....2....3....5....2....2....5
%e ..6....6....4....5....4....6....5....6....5....5....6....5....6....2....4....5
%K nonn
%O 1,1
%A _R. H. Hardin_ Dec 31 2011