%I A005654 M1640
%S A005654 1,2,6,19,66,236,868,3235,12190,46252,176484,676270,2600612,
%T A005654 10030008,38781096,150273315,583407990,2268795980,8836340260,
%U A005654 34461678394,134564560988,526024917288,2058358034616
%N 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.
%D A005654 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005654 Ascher, Marcia; Mu torere: an analysis of a Maori game. Math. Mag. 60 
               (1987), no. 2, 90-100.
%H A005654 F. Ruskey, <a href="http://www.theory.cs.uvic.ca/~cos/inf/neck/NecklaceInfo.html">
               Necklaces, Lyndon words, De Bruijn sequences, etc.</a>
%H A005654 N. J. A. Sloane, <a href="classic.html#LOSS">Classic Sequences</a>
%H A005654 <a href="Sindx_Br.html#bracelets">Index entries for sequences related 
               to bracelets</a>
%F A005654 a(n)= (1/2) (C(2n-1, n)+C(n-1, [ n/2 ])).
%o A005654 (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)!)
%Y A005654 A005654(n)=A034851(2n-1, n-1)
%Y A005654 Sequence in context: A047016 A150084 A150085 this_sequence A150086 A150087 
               A150088
%Y A005654 Adjacent sequences: A005651 A005652 A005653 this_sequence A005655 A005656 
               A005657
%K A005654 nonn,easy,nice
%O A005654 1,2
%A A005654 N. J. A. Sloane (njas(AT)research.att.com).
%E A005654 Sequence extended and description corrected by Christian G. Bower (bowerc(AT)usa.net) 
               Formula from Michael Somos.