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 A045723 Number of configurations, excluding reflections and black-white interchanges, of n black and n white beads on a string. 2
 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 (lc181(AT)york.ac.uk), Apr 28 2006 REFERENCES L. Clarisse and P. Wocjan, On independent permutation separability criteria, Quant. Inf. Comp. 6 277-288, 2006 quant-ph/0504160 LINKS FORMULA (1/4)*(2^n + C(2*n, n) + 2*C(n-1, (1/2)*(n-2))*mod(n+1, 2)). MATHEMATICA Table[ 1/4*(2^n + Binomial[ 2*n, n ] + 2*Binomial[ -1 + n, 1/2*(-2 + n) ]*Mod[ 1 + n, 2 ]), {n, 24} ] CROSSREFS Cf. A042942. Sequence in context: A194691 A148703 A045610 * A140456 A066768 A225914 Adjacent sequences:  A045720 A045721 A045722 * A045724 A045725 A045726 KEYWORD nonn AUTHOR STATUS approved

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