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A182789 Number of n-colorings of the Triangle Graph of order 4. 12
0, 0, 0, 6, 2112, 98820, 1574400, 13676250, 80631936, 363204072, 1342218240, 4261697550, 12000120000, 30653510316, 72237215232, 159067919010, 330577363200, 653537970000, 1236951760896, 2253171240342, 3967187906880, 6776444390100, 11264003520000, 18268445544426 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The Triangle Graph of order 4 has 4 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 10 vertices and 18 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

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

FORMULA

a(n) = n*(n-1)*(n-2)^4*(n^4-9*n^3+31*n^2-49*n+31).

G.f.: -6*x^3*(3267*x^7 +51359*x^6 +195679*x^5 +241075*x^4 +100425*x^3 +12653*x^2 +341*x +1) / (x -1)^11. - Colin Barker, Oct 01 2014

MAPLE

a:= n-> n^10 -18*n^9 +144*n^8 -672*n^7 +2016*n^6 -4031*n^5 +5368*n^4 -4584*n^3 +2272*n^2 -496*n: seq(a(n), n=0..30);

CROSSREFS

4th column of A182797. Cf. A178435, A182798, A182788, A182790, A182791, A182792, A182793, A182794, A182795, A182796.

Sequence in context: A059081 A226461 A172943 * A056048 A051113 A067174

Adjacent sequences:  A182786 A182787 A182788 * A182790 A182791 A182792

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Dec 02 2010

STATUS

approved

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Last modified October 28 17:32 EDT 2021. Contains 348329 sequences. (Running on oeis4.)