A069840 Number of different (unlabeled) 2-cell embeddings of the n-wheel graph W_(n+1) on n+1 nodes into orientable surfaces.

16, 80, 666, 6588, 80886, 1146916, 18583160, 337808300, 6812539360, 150922350288, 3643698427650, 95221941543232, 2678117152113428, 80658585770586368, 2590036811212597862, 88333886984966359596, 3188853320209605353376, 121480126482182314239216, 4870248707151384381179450

Offset

4,1

Comments

Values of a(n) for n <= 3 are not well-defined.

Links

Table of n, a(n) for n=4..22.

B. P. Mull, R. G. Rieper and A. T. White, Enumerating 2-cell imbeddings of connected graphs, Proc. Amer. Math. Soc. 103 (1988), 321-330.

Formula

a(n)=1/(2*n)*sum_(d|n) phi(d)^2*2^(n/d)*(n/d-1)!*d^(n/d-1), n odd; a(n)=1/(2*n)*sum_(d|n) phi(d)^2*2^(n/d)*(n/d-1)!*d^(n/d-1)+ 2^(n-3)*(n/2-1)!, n even, where phi(n) is the Euler totient function A000010.

Mathematica

f[n_] := Block[{d = Divisors[n], s}, s = Apply[Plus, EulerPhi[d]^2*2^(n/d)*(n/d - 1)!*d^(n/d - 1)]/(2n); If[ EvenQ[n], s = s + 2^(n - 3)*(n/2 - 1)! ]; s];

Prog

(PARI) a(n) = 1/(2*n)*sumdiv(n, d, eulerphi(d)^2*2^(n/d)*(n/d-1)!*d^(n/d-1)) + if (!(n % 2), 2^(n-3)*(n/2-1)!); \\ Michel Marcus, May 30 2019

Crossrefs

Cf. A000010, A069839.

Sequence in context: A034570 A165963 A221910 * A000817 A192510 A119508

Adjacent sequences: A069837 A069838 A069839 * A069841 A069842 A069843

Keyword

nonn

Author

Valery A. Liskovets, Apr 22 2002

Extensions

Edited and extended by Robert G. Wilson v and Vladeta Jovovic, May 04 2002

More terms from Michel Marcus, May 30 2019

Status

approved