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 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 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 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. [Cached copy, with permission, pdf format only] N. J. A. Sloane, Classic Sequences FORMULA a(n) = (1/2) * (binomial(2*n-1, n) + binomial(n-1, floor(n/2))). - Michael Somos a(n) = A034851(2*n-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 MAPLE A005654:=n->(1/2)*(binomial(2*n-1, n)+binomial(n-1, floor(n/2))): seq(A005654(n), n=1..40); # Wesley Ivan Hurt, Jan 29 2017 MATHEMATICA Table[(Binomial[2n-1, n]+Binomial[n-1, Floor[n/2]])/2, {n, 30}] (* Harvey P. Dale, May 17 2012 *) PROG (PARI) C(n, k)=binomial(n, k) a(n)=(1/2)*(C(2*n-1, n)+C(n-1, n\2)) (MAGMA) [((Binomial(2*n-1, n)+Binomial(n-1, Floor(n/2)))/2): n in [1..30]]; // Vincenzo Librandi, May 24 2012 CROSSREFS Cf. A034851. Sequence in context: A150085 A306175 A266466 * A150086 A150087 A150088 Adjacent sequences:  A005651 A005652 A005653 * A005655 A005656 A005657 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Sequence extended and description corrected by Christian G. Bower STATUS approved

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Last modified May 24 19:14 EDT 2020. Contains 334580 sequences. (Running on oeis4.)