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

Author

Vladeta Jovovic, Sep 28 2002

Keywords

• easy
• nonn

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).

Crossrefs

Column k=6 of A256067, A256554.

Programs

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 *)

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).