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
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
KEYWORD
nonn,easy,fini,full
AUTHOR
Marko Riedel, Mar 24 2016
STATUS
approved