A074752 Number of combinatorially inequivalent cyclic subgroups of S_n of order 6. Number of partitions of n of order 6.

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

Alois P. Heinz, Table of n, a(n) for n = 5..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,2,-1,-1,0,1,1,-1).

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

Adjacent sequences: A074749 A074750 A074751 * A074753 A074754 A074755

Keyword

easy,nonn

Author

Vladeta Jovovic, Sep 28 2002

Status

approved