OFFSET
1,2
COMMENTS
A finite sequence is normal if it spans an initial interval of positive integers. It is aperiodic if every cyclic rotation is different.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
EXAMPLE
The a(3) = 12 aperiodic normal sequences are 112, 121, 122, 123, 132, 211, 212, 213, 221, 231, 312, 321.
The 15 non-aperiodic normal sequences of length 6 are: 111111, 112112, 121121, 121212, 122122, 123123, 132132, 211211, 212121, 212212, 213213, 221221, 231231, 312312, 321321.
MATHEMATICA
Table[DivisorSum[n, MoebiusMu[n/#]*Sum[k!*StirlingS2[#, k], {k, #}]&], {n, 25}]
PROG
(PARI) \\ here b(n) is A000670.
b(n)={polcoef(serlaplace(1/(2-exp(x+O(x*x^n)))), n)}
a(n)={sumdiv(n, d, moebius(d)*b(n/d))} \\ Andrew Howroyd, Aug 29 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 22 2017
STATUS
approved