%I #34 Sep 18 2024 06:56:08
%S 67,117,181,260,355,467,597,746,915,1105,1317,1552,1811,2095,2405,
%T 2742,3107,3501,3925,4380,4867,5387,5941,6530,7155,7817,8517,9256,
%U 10035,10855,11717,12622,13571,14565,15605,16692,17827,19011,20245,21530,22867,24257
%N Number of nondecreasing arrangements of 6 numbers x(i) in -(n+4)..(n+4) with the sum of sign(x(i))*2^|x(i)| zero.
%H Manuel Kauers and Christoph Koutschan, <a href="/A187990/b187990.txt">Table of n, a(n) for n = 0..1000</a> (terms 1..50 from R. H. Hardin).
%H M. Kauers and C. Koutschan, <a href="https://arxiv.org/abs/2303.02793">Some D-finite and some possibly D-finite sequences in the OEIS</a>, arXiv:2303.02793 [cs.SC], 2023.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = (n^3 + 39*n^2 + 260*n + 402)/6. - _Manuel Kauers_ and _Christoph Koutschan_, Mar 01 2023
%F G.f.: -(-67+151*x-115*x^2+30*x^3)/(x-1)^4. - _R. J. Mathar_, Apr 30 2023
%e Some solutions for n=3
%e -2 -5 -6 -5 -7 -6 -4 -4 -6 -5 -7 -6 -3 -6 -3 -7
%e -1 -4 -5 -1 -6 -3 -3 -2 -6 -4 -3 -6 -3 -3 -3 -5
%e 0 -4 4 -1 5 -2 -3 -1 -5 -1 1 5 -3 -3 -2 -3
%e 0 4 4 2 5 -2 -1 -1 4 1 1 5 2 3 1 3
%e 1 4 5 4 6 4 1 3 4 4 2 5 2 3 1 5
%e 1 5 5 4 6 6 5 4 7 5 7 5 4 6 4 7
%Y Row 6 of A187988.
%K nonn,easy
%O 0,1
%A _R. H. Hardin_, Mar 18 2011
%E a(27) corrected by _Manuel Kauers_ and _Christoph Koutschan_, Mar 01 2023