A051625 - OEIS

This site is supported by donations to The OEIS Foundation.

A051625

Number of "labeled" cyclic subgroups of symmetric group S_n.

1, 2, 5, 17, 67, 362, 2039, 14170, 109694, 976412, 8921002, 101134244, 1104940280, 13914013024, 191754490412, 2824047042632, 41304021782824, 708492417746000, 11629404776897384, 222093818836736752, 4351196253952132832 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,2`
	COMMENTS	`Number of unordered lists of powers of permutation of length n (equivalent to the definition). [Olivier Gerard, Jul 04 2011]` `Number of subgroups of S_n with different permutations generated by single permutation (see Mathematica procedure). - Artur Jasinski, Oct 27 2011`
	REFERENCES	`V. Jovovic, Some combinatorial characteristics of symmetric and alternating groups (in Russian), Belgrade, 1980, unpublished.`
	FORMULA	`a(n) = Sum_{pi} n!/(k_1!1^k_1k_2!2^k_2...k_n!n^k_nphi(lcm{i:k_i != 0})), where pi runs through all partitions k_1+2k_2+...+n*k_n=n and phi is Euler's function.`
	MATHEMATICA	cc = {}; Do[aa = {}; kk = Table[n, {n, 1, ord}]; pp = Permutations[kk]; Do[per17 = {}; AppendTo[per17, pp[[p]]]; run = 0; ile = Length[per17]; min = 1; max = ile; While[ile < ord!, run = run + 1; if = False; Do[Do[vec0 = Table[0, {n, 1, ord}]; Do[vec0[[per17[[k]][[n]]]] = per17[[m]][[n]], {n, 1, ord}]; bp = vec0; If[Position[per17, bp] == {}, ile = ile + 1; Print[ile]; if = True; AppendTo[per17, bp]]; vec0 = Table[0, {n, 1, ord}]; Do[vec0[[per17[[m]][[n]]]] = per17[[k]][[n]], {n, 1, ord}]; bl = vec0; If[Position[per17, bl] == {}, ile = ile + 1; if = True; AppendTo[per17, bl]]; If[ile == ord!, Break[]], {k, 1, max}], {m, min, max}]; If[if == False, Break[], min = max + 1; max = ile]]; AppendTo[aa, Sort[per17]], {p, 1, ord!}]; AppendTo[cc, Length[Union[aa]]], {ord, 1, 7}]; cc (* Artur Jasinski, Oct 27 2011 *)
	CROSSREFS	`Cf. A051636, A000110.` `Sequence in context: A166474 A054769 A003510 * A056098 A027361 A101971` `Adjacent sequences: A051622 A051623 A051624 * A051626 A051627 A051628`
	KEYWORD	`nonn`
	AUTHOR	`Vladeta Jovovic (vladeta(AT)eunet.rs)`

Content is available under The OEIS End-User License Agreement .

Last modified February 17 00:09 EST 2012. Contains 205978 sequences.