cp's OEIS Frontend

A182791 Number of n-colorings of the 6 X 6 X 6 triangular grid.

%I A182791 #18 Jan 21 2024 11:52:55
%S A182791 0,0,0,6,718080,4260983940,2175789895680,268832232086250,
%T A182791 13543515506658816,368471361307591080,6399096250242170880,
%U A182791 78976960885082392110,745151003161018080000,5660706546633925834476,35971041412788697313280
%N A182791 Number of n-colorings of the 6 X 6 X 6 triangular grid.
%C A182791 The 6 X 6 X 6 triangular grid has 6 rows with k vertices in row k. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The graph has 21 vertices and 45 edges altogether.
%H A182791 Alois P. Heinz, <a href="/A182791/b182791.txt">Table of n, a(n) for n = 0..1000</a>
%H A182791 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic polynomial</a>
%H A182791 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_graph#Other_kinds">Triangular grid graph</a>
%H A182791 <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (22, -231, 1540, -7315, 26334, -74613, 170544, -319770, 497420, -646646, 705432, -646646, 497420, -319770, 170544, -74613, 26334, -7315, 1540, -231, 22, -1).
%F A182791 a(n) = n^21 -45*n^20 + ... (see Maple program).
%p A182791 a:= n-> n^21 -45*n^20 +965*n^19 -13115*n^18 +126720*n^17 -925528*n^16 +5303300*n^15 -24419511*n^14 +91795611*n^13 -284572218*n^12 +731723164*n^11 -1563764362*n^10 +2773460910*n^9 -4060976822*n^8 +4861918772*n^7 -4686537246*n^6 +3551696188*n^5 -2039006608*n^4 +833782816*n^3 -216349280*n^2 +26756288*n: seq(a(n), n=0..30);
%Y A182791 6th column of A182797. Cf. A178435, A182798, A182788, A182789, A182790, A182792, A182793, A182794, A182795, A182796.
%K A182791 nonn,easy
%O A182791 0,4
%A A182791 _Alois P. Heinz_, Dec 02 2010