A270842 Number of nonisomorphic edge colorings of the Petersen graph with at most n colors.

1, 396, 123786, 9002912, 254721400, 3920311044, 39571426713, 293231076608, 1715840171595, 8333541708700, 34810892718492, 128392921513440, 426551317876970, 1296405100924948, 3649123762524675, 9607693522053120, 23853550135649477, 56222046462953772

Offset

1,2

Comments

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

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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.

a(n) = n^15/120 + 5*n^9/24 + 5*n^5/12 + 11*n^3/30.

G.f.: x*(1 + 380*x + 117570*x^2 + 7069296*x^3 + 125309188*x^4 + 856514276*x^5 + 2594956089*x^6 + 3729352800*x^7 + 2594956089*x^8 + 856514276*x^9 + 125309188*x^10 + 7069296*x^11 + 117570*x^12 + 380*x^13 + x^14) / (1 - x)^16. - Colin Barker, Dec 24 2017

Prog

(PARI) a(n) = n^15/120 + 5*n^9/24 + 5*n^5/12 + 11*n^3/30; \\ Altug Alkan, Mar 25 2016

Crossrefs

Cf. A270843, A063843. See A159233 for edge colorings where adjacent edges must have different colors.

Sequence in context: A230732 A034621 A203926 * A074483 A023326 A139385

Adjacent sequences: A270839 A270840 A270841 * A270843 A270844 A270845

Keyword

nonn,easy

Author

Marko Riedel, Mar 24 2016

Status

approved