OFFSET
1,4
COMMENTS
Turning over the necklace is not allowed. Colors may be permuted without changing the necklace structure.
Identical to A000048 for n>1.
Number of binary Lyndon words of length n with an odd number of zeros. - Joerg Arndt, Oct 26 2015
REFERENCES
M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
PROG
(PARI) vector(100, n, sumdiv(n, d, (d%2)*(moebius(d)*2^(n/d)))/(2*n)-!(n-1)) \\ Altug Alkan, Oct 26 2015
(Python)
from sympy import divisors, mobius
def a000048(n): return 1 if n<1 else sum([mobius(d)*2**(n/d) for d in divisors(n) if d%2 == 1])/(2*n)
def a(n): return a000048(n) - 0**(n - 1) # Indranil Ghosh, Apr 28 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved