cp's OEIS Frontend

A265234 Number of 4 X n arrays containing n copies of 0..4-1 with no equal vertical neighbors and new values introduced sequentially from 0.

%I A265234 #23 Mar 08 2023 03:05:54
%S A265234 1,43,2592,184740,14439456,1196114464,103142395392,9160513923648,
%T A265234 832211576040960,76971887847571968,7223525356855099392,
%U A265234 686117529041422350336,65834293657115919826944,6371837299781950752276480
%N A265234 Number of 4 X n arrays containing n copies of 0..4-1 with no equal vertical neighbors and new values introduced sequentially from 0.
%H A265234 Manuel Kauers and Christoph Koutschan, <a href="/A265234/b265234.txt">Table of n, a(n) for n = 1..495</a> (terms 1..31 from R. H. Hardin).
%H A265234 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.
%F A265234 From _Manuel Kauers_ and _Christoph Koutschan_, Mar 01 2023: (Start)
%F A265234 a(n) = coefficient of x^n*y^n*z^n in (1/24)*(2*x^2 + 6*x*y + 6*x^2*y + 2*y^2 + 6*x*y^2 + 2*x^2*y^2 + 6*x*z + 6*x^2*z + 6*y*z + 24*x*y*z + 6*x^2*y*z + 6*y^2*z + 6*x*y^2*z + 2*z^2 + 6*x*z^2 + 2*x^2*z^2 + 6*y*z^2 + 6*x*y*z^2 + 2*y^2*z^2)^n.
%F A265234 Recurrence of order 6 and degree 6: 5*(n + 5)*(832*n^2 + 5785*n + 8460)*(n + 6)^3*a(n + 6) - 4*(n + 5)*(126464*n^5 + 2941016*n^4 + 26840735*n^3 + 119399663*n^2 + 256228730*n + 208319000)*a(n + 5) + 16*(310336*n^6 + 7680621*n^5 + 78610375*n^4 + 426421788*n^3 + 1294537774*n^2 + 2087600280*n + 1398239904)*a(n + 4) + 128*(n + 4)*(1161472*n^5 + 24822356*n^4 + 207271023*n^3 + 841828441*n^2 + 1653171497*n + 1242989235)*a(n + 3) - 768*(n + 3)*(n + 4)*(3709888*n^4 + 58438003*n^3 + 333112832*n^2 + 813878537*n + 716118600)*a(n + 2) + 9216*(n + 2)*(n + 3)*(n + 4)*(1743872*n^3 + 20496944*n^2 + 74692297*n + 84692065)*a(n + 1) - 34836480*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(832*n^2 + 7449*n + 15077)*a(n) = 0. (End)
%F A265234 a(n) ~ 2^(2*n - 19/2) * 3^(3*n + 7/2) / (Pi^(3/2) * n^(3/2)). - _Vaclav Kotesovec_, Mar 08 2023
%e A265234 Some solutions for n=4:
%e A265234   0  0  1  2    0  1  0  1    0  1  0  2    0  0  1  2    0  1  1  2
%e A265234   3  3  0  3    2  3  3  2    2  2  3  3    3  3  3  1    3  2  3  1
%e A265234   2  0  1  1    1  0  2  3    1  0  1  1    2  1  0  0    1  0  0  0
%e A265234   1  2  2  3    3  1  0  2    0  3  2  3    3  2  2  1    3  2  3  2
%Y A265234 Row 4 of A265232.
%K A265234 nonn
%O A265234 1,2
%A A265234 _R. H. Hardin_, Dec 06 2015