OFFSET
1,3
REFERENCES
F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.
LINKS
Marko Riedel et al., Burnside lemma and translational symmetries of the torus.
Marko Riedel, Maple code for sequence.
FORMULA
a(n) = (1/(n^2*4!))*(Sum_{sigma in S_4} Sum_{d|n} Sum_{f|n} phi(d) phi(f) [[forall j_l(sigma) > 0 : l|lcm(d,f) ]] P(gcd(d,f)*(n/d)*(n/f), sigma)) where P(F, sigma) = F! [z^F] Product_{l=1..4} (exp(lz)-1)^j_l(sigma). The notation j_l(sigma) is from the Harary text and gives the number of cycles of length l in the permutation sigma. [[.]] is an Iverson bracket.
CROSSREFS
KEYWORD
nonn
AUTHOR
Marko Riedel, Oct 03 2024
STATUS
approved