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A007727 Number of 2n-bead black-white strings with n black beads and fundamental period 2n. 8
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

Table of n, a(n) for n=0..24.

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 * A226011 A052689 A139104

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 February 25 22:18 EST 2018. Contains 299662 sequences. (Running on oeis4.)