|
|
A069840
|
|
Number of different (unlabeled) 2-cell embeddings of the n-wheel graph W_(n+1) on n+1 nodes into orientable surfaces.
|
|
1
|
|
|
16, 80, 666, 6588, 80886, 1146916, 18583160, 337808300, 6812539360, 150922350288, 3643698427650, 95221941543232, 2678117152113428, 80658585770586368, 2590036811212597862, 88333886984966359596, 3188853320209605353376, 121480126482182314239216, 4870248707151384381179450
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
4,1
|
|
COMMENTS
|
Values of a(n) for n <= 3 are not well-defined.
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|