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 A045723 Number of configurations, excluding reflections and black-white interchanges, of n black and n white beads on a string. 7
 1, 1, 3, 7, 23, 71, 252, 890, 3299, 12283, 46508, 176870, 677294, 2602198, 10034104, 38787572, 150289699, 583434323, 2268861516, 8836447022, 34461940538, 134564992898, 526025965864, 2058359779052, 8061905791118, 31602659998046 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This sequence (with offset 0) equals the probable number of inequivalent classes of permutations acting on an n-party state under the trace norm in the context of permutation criteria for separability. - Lieven Clarisse, Apr 28 2006 Number of connected components of an undirected graph where the nodes are the n-subsets of {1,...,2n} and an edge (A,B) appears if B = {1,...,2n} \ A or B = {2n + 1 - i: i in A}. See Mathematics Magazine link. - Rob Pratt, Aug 10 2015 Number of distinct staircase walks connecting opposite corners of a square grid of side n > 1. - Christian Barrientos, Nov 25 2018 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Eddie Cheng and Jerrold W. Grossman, Problem 1959, Mathematics Magazine 87 (Dec. 2014), p. 396. L. Clarisse and P. Wocjan, On independent permutation separability criteria, Quant. Inf. Comp. 6 277-288, 2006, arXiv:quant-ph/0504160, 2005. FORMULA a(n) = (1/4)*(2^n + C(2*n, n) + 2*C(n-1, (1/2)*(n-2))*((n+1) mod 2)). a(n) = A042971(n) + A027306(n). - Michel Marcus, Nov 26 2018 MATHEMATICA Table[ 1/4 (2^n + Binomial[ 2 n, n ] + 2 Binomial[ -1 + n, 1/2 (-2 + n) ]*Mod[ 1 + n, 2 ]), {n, 0, 24} ] PROG (PARI) a(n) = (1/4)*(2^n + binomial(2*n, n) + if ((n+1)%2, 2*binomial(n-1, (1/2)*(n-2)))); \\ Michel Marcus, Nov 25 2018 CROSSREFS Cf. A042942. Cf. A027306, A042971. Sequence in context: A148703 A302180 A045610 * A140456 A066768 A225914 Adjacent sequences:  A045720 A045721 A045722 * A045724 A045725 A045726 KEYWORD nonn AUTHOR STATUS approved

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Last modified May 31 00:29 EDT 2020. Contains 334747 sequences. (Running on oeis4.)