login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A032296 Number of aperiodic bracelets (turn over necklaces) with n beads of 5 colors. 1
5, 10, 30, 105, 372, 1460, 5890, 25275, 110050, 492744, 2227270, 10195070, 46989180, 218096780, 1017447736, 4768944375, 22440372240, 105966686200, 501938733550, 2384200190580, 11353290083380 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..21.

C. G. Bower, Transforms (2)

F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.

N. J. A. Sloane, Transforms

Index entries for sequences related to bracelets

FORMULA

MOEBIUS transform of A032276.

From Herbert Kociemba, Nov 28 2016: (Start)

More generally, gf(k) is the g.f. for the number of bracelets with primitive period n and beads of k colors.

gf(k): Sum_{n>=1} mu(n)*( -log(1-k*x^n)/n + Sum_{i=0..2} binomial(k,i)x^(n*i)/(1-k*x^(2*n)) )/2. (End)

MATHEMATICA

mx=40; gf[x_, k_]:=Sum[ MoebiusMu[n]*(-Log[1-k*x^n]/n+Sum[Binomial[k, i]x^(n i), {i, 0, 2}]/( 1-k x^(2n)))/2, {n, mx}]; CoefficientList[Series[gf[x, 5], {x, 0, mx}], x] (* Herbert Kociemba, Nov 28 2016 *)

CROSSREFS

Column 5 of A276550.

Sequence in context: A077916 A189315 A056422 * A052648 A020995 A174467

Adjacent sequences:  A032293 A032294 A032295 * A032297 A032298 A032299

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 23 07:28 EST 2018. Contains 299473 sequences. (Running on oeis4.)