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

1,4

Comments

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

Links

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

Formula

Moebius transform of A326895.

Example

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

Prog

(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)))}

Crossrefs

Row sums of A309651.

Cf. A309528.

Sequence in context: A052571 A324074 A052625 * A326895 A291033 A155130

Adjacent sequences: A326885 A326886 A326887 * A326889 A326890 A326891

Keyword

nonn

Author

Andrew Howroyd, Sep 12 2019

Status

approved