

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
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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.
Inclusionexclusion 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



