cp's OEIS Frontend

A215191 Number of arrays of 4 0..n integers with no sum of consecutive elements equal to a disjoint adjacent sum of an equal number of elements.

%I A215191 #10 Jul 22 2018 12:32:12
%S A215191 0,18,88,276,664,1366,2512,4264,6800,10330,15080,21308,29288,39326,
%T A215191 51744,66896,85152,106914,132600,162660,197560,237798,283888,336376,
%U A215191 395824,462826,537992,621964,715400,818990,933440,1059488,1197888,1349426
%N A215191 Number of arrays of 4 0..n integers with no sum of consecutive elements equal to a disjoint adjacent sum of an equal number of elements.
%C A215191 Row 4 of A215190.
%H A215191 R. H. Hardin, <a href="/A215191/b215191.txt">Table of n, a(n) for n = 1..210</a>
%F A215191 Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6).
%F A215191 Conjectures from _Colin Barker_, Jul 22 2018: (Start)
%F A215191 G.f.: 2*x^2*(9 + 8*x + 7*x^2) / ((1 - x)^5*(1 + x)).
%F A215191 a(n) = n*(3*n^3 + n^2 - 1)/3 for n even.
%F A215191 a(n) = (3*n^4 + n^3 - n - 3)/3 for n odd.
%F A215191 (End)
%e A215191 Some solutions for n=6:
%e A215191   2  4  6  0  0  6  6  2  0  0  1  6  5  4  3  3
%e A215191   4  3  0  4  5  0  1  3  2  4  4  0  6  5  4  5
%e A215191   1  5  4  0  1  6  2  5  5  1  3  4  2  6  0  3
%e A215191   0  1  6  3  3  3  3  1  4  5  0  3  0  0  3  4
%Y A215191 Cf. A215190.
%K A215191 nonn
%O A215191 1,2
%A A215191 _R. H. Hardin_, Aug 05 2012