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%I #8 Jun 04 2018 03:35:56
%S 5,21,69,188,444,944,1844,3369,5825,9621,15285,23492,35080,51084,
%T 72756,101601,139401,188257,250613,329304,427584,549176,698304,879749,
%U 1098881,1361721,1674977,2046108,2483364,2995856,3593596,4287573,5089797,6013377
%N Number of arrays of 2n nondecreasing integers in -4..4 with sum zero and equal numbers greater than zero and less than zero.
%C Column 4 of A203291.
%H R. H. Hardin, <a href="/A203287/b203287.txt">Table of n, a(n) for n = 1..189</a>
%F Empirical: a(n) = 4*a(n-1) -4*a(n-2) -3*a(n-3) +6*a(n-4) -6*a(n-7) +3*a(n-8) +4*a(n-9) -4*a(n-10) +a(n-11).
%F Empirical g.f.: x*(5 + x + 5*x^2 + 11*x^3 + x^4 + x^5 - 6*x^6 + 3*x^7 + 4*x^8 - 4*x^9 + x^10) / ((1 - x)^7*(1 + x)^2*(1 + x + x^2)). - _Colin Barker_, Jun 04 2018
%e Some solutions for n=3:
%e .-3...-1...-3...-3...-3...-3...-3...-4...-3...-4...-4...-3...-2...-4...-4...-4
%e .-3...-1...-2...-3...-2...-3...-3...-1...-2....0...-2...-1....0...-2...-2...-4
%e .-1...-1....0...-2...-1...-1...-1...-1....0....0...-1...-1....0...-2...-1...-1
%e ..1....1....0....1....1....1....2....1....0....0....1....1....0....2....2....3
%e ..3....1....2....3....1....2....2....2....1....0....2....2....0....3....2....3
%e ..3....1....3....4....4....4....3....3....4....4....4....2....2....3....3....3
%Y Cf. A203291.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 31 2011
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