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A182792 Number of n-colorings of the Triangle Graph of order 7. 12
0, 0, 0, 6, 22665216, 3013780700340, 14668353488732160, 10142843465859326250, 2047585083571827265536, 177922459478738381782536, 8379024937788205785415680, 247855358008532074713890670, 5089690042011600555045120000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The Triangle Graph of order 7 has 7 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 28 vertices and 63 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^28 -63*n^27 + ... (see Maple program).

MAPLE

a:= n-> n^28 -63*n^27 +1917*n^26 -37515*n^25 +530415*n^24 -5770367*n^23 +50229001*n^22 -359161581*n^21 +2149154827*n^20 -10907730408*n^19 +47421892719*n^18 -177879720291*n^17 +578605822984*n^16 -1637514420168*n^15 +4039146735437*n^14 -8685828617404*n^13 +16263806276269*n^12 -26442885506316*n^11 +37160408393135*n^10 -44834641208000*n^9 +46004737388704*n^8 -39623922744400*n^7

+28128173982016*n^6 -16032767219808*n^5 +7056432341248*n^4 -2251430597120*n^3 +463382611200*n^2 -46172626432*n: seq(a(n), n=0..30);

CROSSREFS

7th column of A182797. Cf. A178435, A182798, A182788, A182789, A182790, A182791, A182793, A182794, A182795, A182796.

Sequence in context: A269516 A116272 A273723 * A067484 A337083 A193150

Adjacent sequences:  A182789 A182790 A182791 * A182793 A182794 A182795

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.)