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A270843 Number of nonisomorphic edge colorings of the Petersen graph with exactly n colors. 1
1, 394, 122601, 8510140, 210940745, 2524556538, 17167621086, 72787256640, 202996629360, 382918536000, 492133561920, 424994169600, 236107872000, 76281004800, 10897286400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is zero when n is more than fifteen because only fifteen edges are available.

These are not colorings in the strict sense, since there is no requirement that adjacent edges have different colors. - N. J. A. Sloane, Mar 28 2016

The value for n=15 is 15!/120 because all orbits are the same size namely 120 (order of the symmetric group on five elements) when each of the 15 edges has a unique color. - Marko Riedel, Mar 28 2016

LINKS

Table of n, a(n) for n=1..15.

Math StackExchange, Edge colorings of the Petersen graph

FORMULA

Cycle index of the automorphisms acting on the edges is (1/120)*S[1]^15+(5/24)*S[2]^6*S[1]^3+(1/4)*S[4]^3*S[2]*S[1]+(1/6)*S[3]^5+(1/6)*S[3]*S[6]^2+(1/5)*S[5]^3.

Inclusion-exclusion yields a(n) = sum(C(n, q)*(-1)^q*A270842(n - q), q = 0 .. n)

CROSSREFS

Cf. A270842, A063843.

Sequence in context: A051986 A223908 A251256 * A267965 A268030 A278610

Adjacent sequences:  A270840 A270841 A270842 * A270844 A270845 A270846

KEYWORD

nonn,easy,fini,full

AUTHOR

Marko Riedel, Mar 24 2016

STATUS

approved

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Last modified May 26 13:59 EDT 2022. Contains 354092 sequences. (Running on oeis4.)