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A326888
Number of length n asymmetric bracelets with integer entries that cover an initial interval of positive integers.
3
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
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Sep 12 2019
STATUS
approved