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 A007727 Number of 2n-bead black-white strings with n black beads and fundamental period 2n. 13
 1, 2, 4, 18, 64, 250, 900, 3430, 12800, 48600, 184500, 705430, 2703168, 10400598, 40113164, 155117250, 601067520, 2333606218, 9075085776, 35345263798, 137846344000, 538257870990, 2104098258284, 8233430727598, 32247600966144 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n>0, a(n) is divisible by n^2 (cf. A268619) and 6*a(n) is divisible by n^3 (cf. A268592). - Max Alekseyev, Feb 07 2016 LINKS Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1. FORMULA For n>0, a(n) = Sum_{d|n} A008683(n/d)*A000984(d). For n>0, a(n) = 2 * A045630(n). a(0)=1, a(n) = n * A060165(n) = 2n * A022553(n). - Ralf Stephan, Sep 01 2003 PROG (PARI) { a(n) = if(n>0, sumdiv(n, d, moebius(n/d)*binomial(2*d, d)), 0); } CROSSREFS Cf. A045630, A060165, A022553. Sequence in context: A179040 A241685 A009679 * A303352 A226011 A325850 Adjacent sequences:  A007724 A007725 A007726 * A007728 A007729 A007730 KEYWORD nonn AUTHOR Doug Bowman, bowman(AT)math.uiuc.edu. EXTENSIONS Edited by Max Alekseyev, Feb 09 2016 STATUS approved

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Last modified April 8 08:54 EDT 2020. Contains 333313 sequences. (Running on oeis4.)