|
%I #18 Jan 21 2024 11:52:55
%S 0,0,0,6,718080,4260983940,2175789895680,268832232086250,
%T 13543515506658816,368471361307591080,6399096250242170880,
%U 78976960885082392110,745151003161018080000,5660706546633925834476,35971041412788697313280
%N Number of n-colorings of the 6 X 6 X 6 triangular grid.
%C 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 Alois P. Heinz, <a href="/A182791/b182791.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic polynomial</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_graph#Other_kinds">Triangular grid graph</a>
%H <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 a(n) = n^21 -45*n^20 + ... (see Maple program).
%p 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 6th column of A182797. Cf. A178435, A182798, A182788, A182789, A182790, A182792, A182793, A182794, A182795, A182796.
%K nonn,easy
%O 0,4
%A _Alois P. Heinz_, Dec 02 2010
|
