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A007727 Number of 2n-bead black-white strings with n black beads and fundamental period 2n. 14
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
MAPLE
A007727 := proc(n)
if n = 0 then
1;
else
add(numtheory[mobius](n/d)*binomial(2*d, d), d =numtheory[divisors](n)) ;
end if ;
end proc:
seq(A007727(n), n=0..10) ; # R. J. Mathar, Nov 10 2021
MATHEMATICA
a[n_] := If[n == 0, 1, Sum[MoebiusMu[n/d] Binomial[2d, d], {d, Divisors[n]}]];
Table[a[n], {n, 0, 24}] (* Jean-François Alcover, May 05 2023 *)
PROG
(PARI) { a(n) = if(n>0, sumdiv(n, d, moebius(n/d)*binomial(2*d, d)), 0); }
CROSSREFS
Sequence in context: A179040 A241685 A009679 * A303352 A226011 A174085
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 March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)