OFFSET
1,3
COMMENTS
Colors are not being permuted, i.e., Power Group Enumeration does not apply here.
REFERENCES
F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..820 (first 40 rows)
Marko Riedel et al., Burnside lemma and translational symmetries of the torus.
FORMULA
T(n,k) = (Q!/(n*k))*(Sum_{d|n} Sum_{f|k} phi(d) phi(f) S(gcd(d,f)*(n/d)*(k/f), Q)) with Q=3 and S(n,k) Stirling numbers of the second kind.
EXAMPLE
Triangle begins:
0;
0, 9;
2, 91, 2022;
9, 738, 43315, 2679246;
30, 5613, 950062, 174184755, 33887517990;
91, 43404, 21480921, 11765865678, 6862930841141, 4169289730628814;
...
PROG
(PARI) T(n, m)=6*sumdiv(n, d, sumdiv(m, e, eulerphi(d) * eulerphi(e) * stirling(n*m/lcm(d, e), 3, 2) ))/(n*m) \\ Andrew Howroyd, Oct 05 2024
CROSSREFS
KEYWORD
AUTHOR
Marko Riedel, Nov 06 2017
STATUS
approved