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

0, 0, 0, 6, 718080, 4260983940, 2175789895680, 268832232086250, 13543515506658816, 368471361307591080, 6399096250242170880, 78976960885082392110, 745151003161018080000, 5660706546633925834476, 35971041412788697313280

Offset

0,4

Comments

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.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Chromatic polynomial

Wikipedia, Triangular grid graph

Index entries for linear recurrences with constant coefficients, signature (22, -231, 1540, -7315, 26334, -74613, 170544, -319770, 497420, -646646, 705432, -646646, 497420, -319770, 170544, -74613, 26334, -7315, 1540, -231, 22, -1).

Formula

a(n) = n^21 -45*n^20 + ... (see Maple program).

Maple

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);

Crossrefs

6th column of A182797. Cf. A178435, A182798, A182788, A182789, A182790, A182792, A182793, A182794, A182795, A182796.

Sequence in context: A072234 A369973 A172823 * A336397 A235589 A340183

Adjacent sequences: A182788 A182789 A182790 * A182792 A182793 A182794

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 02 2010

Status

approved