cp's OEIS Frontend

A203293 Number of arrays of 6 nondecreasing integers in -n..n with sum zero and equal numbers greater than zero and less than zero.

%I A203293 #8 Jun 04 2018 05:47:46
%S A203293 4,10,28,69,154,310,580,1013,1680,2662,4064,6005,8634,12114,16644,
%T A203293 22441,29760,38878,50116,63817,80374,100206,123784,151609,184240,
%U A203293 222266,266340,317149,375446,442022,517740,603501,700284,809110,931080,1067341,1219126
%N A203293 Number of arrays of 6 nondecreasing integers in -n..n with sum zero and equal numbers greater than zero and less than zero.
%C A203293 Row 3 of A203291.
%H A203293 R. H. Hardin, <a href="/A203293/b203293.txt">Table of n, a(n) for n = 1..210</a>
%F A203293 Empirical: a(n) = 3*a(n-1) -a(n-2) -4*a(n-3) +2*a(n-4) +2*a(n-5) +2*a(n-6) -4*a(n-7) -a(n-8) +3*a(n-9) -a(n-10).
%F A203293 Empirical g.f.: x*(4 - 2*x + 2*x^2 + 11*x^3 + 7*x^4 + x^5 - 4*x^6 + x^7 + 3*x^8 - x^9) / ((1 - x)^6*(1 + x)^2*(1 + x + x^2)). - _Colin Barker_, Jun 04 2018
%e A203293 Some solutions for n=3:
%e A203293 .-2...-2...-2...-3...-3...-1...-3...-3....0...-2...-1...-3...-2...-3...-3...-3
%e A203293 ..0...-2...-2...-2...-1...-1....0...-3....0...-2...-1...-2...-2...-2...-1...-1
%e A203293 ..0....0...-1....0....0...-1....0...-1....0....0....0...-2...-2...-1....0...-1
%e A203293 ..0....0....1....0....0....1....0....2....0....0....0....2....2....2....0....1
%e A203293 ..0....1....2....2....2....1....0....2....0....2....1....2....2....2....1....1
%e A203293 ..2....3....2....3....2....1....3....3....0....2....1....3....2....2....3....3
%Y A203293 Cf. A203291.
%K A203293 nonn
%O A203293 1,1
%A A203293 _R. H. Hardin_, Dec 31 2011