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A182791 Number of n-colorings of the Triangle Graph of order 6. 12
0, 0, 0, 6, 718080, 4260983940, 2175789895680, 268832232086250, 13543515506658816, 368471361307591080, 6399096250242170880, 78976960885082392110, 745151003161018080000, 5660706546633925834476, 35971041412788697313280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The Triangle Graph of order 6 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

Eric Weisstein's World of Mathematics, Triangle Graph

Wikipedia, Chromatic polynomial

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: A079288 A072234 A172823 * A336397 A235589 A340183

Adjacent sequences:  A182788 A182789 A182790 * A182792 A182793 A182794

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 02 2010

STATUS

approved

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)