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 A005656 Number of bracelets (turn over necklaces) with n red, 1 pink and n - 3 blue beads; also reversible strings with n red and n-3 blue beads. (Formerly M2920) 2
 0, 0, 1, 3, 12, 44, 170, 651, 2520, 9752, 37854, 147070, 572264, 2229096, 8692788, 33933459, 132594480, 518584880, 2029976630, 7952706234, 31179618184, 122331419080, 480283635468, 1886828198398 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES 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 Marcia Ascher, Mu torere: an analysis of a Maori game, Math. Mag. 60 (1987), no. 2, 90-100. R. K. Guy & N. J. A. Sloane, Correspondence, 1985 F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only] FORMULA a(n) = (1/2)*(binomial(2*n - 3, n - 3) + binomial(n - 2, floor((n - 3)/2))). - Michael Somos MAPLE A005656:=n->(1/2)*(binomial(2*n-3, n-3) + binomial(n-2, floor((n-3)/2))): seq(A005656(n), n=1..30); # Wesley Ivan Hurt, Oct 06 2017 MATHEMATICA Table[(1/2) (Binomial[2 n - 3, n - 3] + Binomial[n - 2, Floor[(n - 3) / 2]]), {n, 40}] (* Vincenzo Librandi, Oct 08 2017 *) PROG (PARI) C(n, k)= if(k<0||k>n, 0, n!/k!/(n-k)!); a(n)= (1/2) *(C(2*n-3, n-3)+C(n-2, (n-3)\2)); (MAGMA) [(1/2)*(Binomial(2*n-3, n-3) + Binomial(n-2, Floor((n-3)/2))): n in [1..30]]; // Vincenzo Librandi, Oct 08 2017 CROSSREFS a(n) = A034851(2n-3, n-3). Sequence in context: A296225 A109437 A331473 * A339066 A260146 A229936 Adjacent sequences:  A005653 A005654 A005655 * A005657 A005658 A005659 KEYWORD nonn AUTHOR EXTENSIONS Sequence corrected, extended and description corrected by Christian G. Bower STATUS approved

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Last modified April 17 06:46 EDT 2021. Contains 343059 sequences. (Running on oeis4.)