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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005654 Number of bracelets (turn over necklaces) with n red, 1 pink and n-1 blue beads; also reversible strings with n red and n-1 blue beads; also next-to-central column in Losanitsch's triangle A034851.
(Formerly M1640)
3
1, 2, 6, 19, 66, 236, 868, 3235, 12190, 46252, 176484, 676270, 2600612, 10030008, 38781096, 150273315, 583407990, 2268795980, 8836340260, 34461678394, 134564560988, 526024917288, 2058358034616, 8061901596814, 31602652961516, 123979635837176, 486734861612328 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Ascher, Marcia; Mu torere: an analysis of a Maori game. Math. Mag. 60 (1987), no. 2, 90-100.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

A. Ivanyi, L. Lucz, T. Matuszka, and S. Pirzada, Parallel enumeration of degree sequences of simple graphs, Acta Univ. Sapientiae, Informatica, 4, 2 (2012) 260-288.

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

N. J. A. Sloane, Classic Sequences

Index entries for sequences related to bracelets

FORMULA

a(n) = (1/2) (C(2n-1, n)+C(n-1, [ n/2 ])).

a(n) = A034851(2n-1,n-1).

Conjecture: n*(n-2)*a(n) -(5*n-3)*(n-2)*a(n-1) +4*(n-2)*a(n-2) +4*(5*n^2-27*n+37)*a(n-3) -8*(2*n-7)*(n-4)*a(n-4)=0. - R. J. Mathar, Nov 09 2013

MATHEMATICA

Table[(Binomial[2n-1, n]+Binomial[n-1, Floor[n/2]])/2, {n, 30}] Harvey P. Dale, May 17 2012

PROG

(PARI) a(n)= (1/2) *(C(2*n-1, n)+C(n-1, n\2)) where C(n, k)=if(k<0|k>n, 0, n!/k!/(n-k)!)

(MAGMA) [((Binomial(2*n-1, n)+Binomial(n-1, Floor(n/2)))/2): n in [1..30]]; // Vincenzo Librandi, May 24 2012

CROSSREFS

Sequence in context: A212380 A150084 A150085 * A150086 A150087 A150088

Adjacent sequences:  A005651 A005652 A005653 * A005655 A005656 A005657

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Sequence extended and description corrected by Christian G. Bower Formula from Michael Somos.

STATUS

approved

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

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

Last modified November 29 00:35 EST 2014. Contains 250479 sequences.