A032179 Number of necklaces with n labeled beads of 3 colors.

3, 9, 54, 486, 5832, 87480, 1574640, 33067440, 793618560, 21427701120, 642831033600, 21213424108800, 763683267916800, 29783647448755200, 1250913192847718400, 56291093678147328000, 2701972496551071744000, 137800597324104658944000, 7441232255501651582976000

Offset

1,1

Links

Table of n, a(n) for n=1..19.

C. G. Bower, Transforms (2)

Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7

Index entries for sequences related to necklaces

Formula

"CIJ" (necklace, indistinct, labeled) transform of 3, 0, 0, 0...

E.g.f.: log(1/(1-3*x)).

a(n) = 3^n * (n-1)!. - Vaclav Kotesovec, Jan 05 2014

D-finite with recurrence: a(n) +3*(-n+1)*a(n-1)=0. - R. J. Mathar, Jan 28 2020

Mathematica

s=3; lst={s}; Do[s+=n*s+s; AppendTo[lst, s], {n, 1, 5!, 3}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
Rest[With[{nn=20}, CoefficientList[Series[Log[1/(1-3x)], {x, 0, nn}], x] Range[0, nn]!]] (* Harvey P. Dale, Sep 22 2011 *)

Prog

(PARI) Vec(serlaplace(log(1/(1-3*'x+O('x^66))))) /* Joerg Arndt, Jan 25 2013 */

Crossrefs

Sequence in context: A337039 A025226 A001194 * A377340 A233189 A175117

Adjacent sequences: A032176 A032177 A032178 * A032180 A032181 A032182

Keyword

nonn,easy

Author

Christian G. Bower

Status

approved