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Search: id:A005654
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| A005654 |
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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)
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+0
2
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| 1, 2, 6, 19, 66, 236, 868, 3235, 12190, 46252, 176484, 676270, 2600612, 10030008, 38781096, 150273315, 583407990, 2268795980, 8836340260, 34461678394, 134564560988, 526024917288, 2058358034616
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Ascher, Marcia; Mu torere: an analysis of a Maori game. Math. Mag. 60 (1987), no. 2, 90-100.
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LINKS
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F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.
N. J. A. Sloane, Classic Sequences
Index entries for sequences related to bracelets
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FORMULA
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a(n)= (1/2) (C(2n-1, n)+C(n-1, [ n/2 ])).
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PROGRAM
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(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)!)
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CROSSREFS
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A005654(n)=A034851(2n-1, n-1)
Sequence in context: A047016 A150084 A150085 this_sequence A150086 A150087 A150088
Adjacent sequences: A005651 A005652 A005653 this_sequence A005655 A005656 A005657
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Sequence extended and description corrected by Christian G. Bower (bowerc(AT)usa.net) Formula from Michael Somos.
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