A326888 Number of length n asymmetric bracelets with integer entries that cover an initial interval of positive integers.

0, 0, 1, 6, 48, 369, 3341, 33960, 393467, 5111052, 73753685, 1170468816, 20263758984, 380047813297, 7676106093000, 166114206886740, 3834434320842720, 94042629507381957, 2442147034668044933, 66942194905675830162, 1931543452344523775050, 58519191359155952404837

Offset: 1

Author

Andrew Howroyd, Sep 12 2019

Keywords

• nonn

Comments

Asymmetric bracelets are those primitive (period n) bracelets that when turned over are different from themselves.

Examples

			For n = 4, the six asymmetric bracelets are  1123, 1223, 1233, 1234, 1243, 1324.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200

Crossrefs

Row sums of A309651.

Cf. A309528.

Programs

PARI

\\ U(n,k) is A309528
U(n,k)={sumdiv(n, d, moebius(n/d)*(k^d/n - if(d%2, k^((d+1)/2), (k+1)*k^(d/2)/2)))/2}
a(n)={sum(k=1, n, U(n,k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)))}

Formula

Moebius transform of A326895.