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A376749
Number of non-isomorphic colorings of a toroidal n X n grid using exactly four swappable colors.
4
0, 1, 874, 10741819, 1870851589562, 5465007068038102643, 269482732023591671431784330, 221537990355601030571170905795094315, 3007205014171762201565124875608675533096268906, 669557518440386985607930852942771727146772232484581602227, 2433673642945425535196140161775877796522974318753784273286700783313050
OFFSET
1,3
REFERENCES
F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.
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
Main diagonal of A294793.
Sequence in context: A045258 A252219 A252212 * A038658 A065700 A297511
KEYWORD
nonn
AUTHOR
Marko Riedel, Oct 03 2024
STATUS
approved