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A074752
Number of combinatorially inequivalent cyclic subgroups of S_n of order 6. Number of partitions of n of order 6.
4
1, 2, 3, 5, 7, 9, 12, 16, 19, 24, 29, 34, 40, 48, 54, 63, 72, 81, 91, 104, 114, 128, 142, 156, 171, 190, 205, 225, 245, 265, 286, 312, 333, 360, 387, 414, 442, 476, 504, 539, 574, 609, 645, 688, 724, 768, 812, 856, 901, 954, 999, 1053, 1107, 1161, 1216, 1280
OFFSET
5,2
COMMENTS
Two permutation groups are combinatorially equivalent iff they have the same cycle index. Order of partition is lcm of its parts.
LINKS
FORMULA
G.f.: x^5*(1+x-x^6)/((x-1)*(x^2-1)*(x^3-1)*(x^6-1)). More generally, g.f. for number of partitions of order d is Sum_{i divides d} mu(d/i)*1/Product_{j divides i} (1-x^j).
MATHEMATICA
LinearRecurrence[{1, 1, 0, -1, -1, 2, -1, -1, 0, 1, 1, -1}, {1, 2, 3, 5, 7, 9, 12, 16, 19, 24, 29, 34}, 60] (* Harvey P. Dale, May 23 2020 *)
CROSSREFS
Column k=6 of A256067, A256554.
Sequence in context: A228896 A281783 A224854 * A039825 A126256 A347646
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Sep 28 2002
STATUS
approved