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A276548 Number of primitive (period n) bracelet structures using an infinite alphabet. 2
1, 1, 2, 5, 11, 33, 92, 347, 1347, 6338, 31949, 179265, 1071264, 6845487, 46162569, 327731596, 2437753739, 18948597836, 153498350744, 1293123237572, 11306475314372, 102425554267565, 959826755336241, 9290811905211847 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = Sum_{d|n} mu(n/d) * A084708(d).
MATHEMATICA
u[0, _] = 1; u[k_, j_] := u[k, j] = Sum[Binomial[k - 1, i - 1] Total[u[k - i, j] #^(i - 1) & /@ Divisors[j]], {i, k}];
b[n_] := 1/n*Total[EulerPhi[#] u[Quotient[n, #], #]& /@ Divisors[n] ];
A084708[n_] := b[n]/2 + If[EvenQ[n], u[n/2, 2], Sum[Binomial[n/2 - 1/2, k] u[k, 2], {k, 0, n/2 - 1/2}]]/2;
a[n_] := Sum[MoebiusMu[n/d]*A084708[d], {d, Divisors[n]}];
Array[a, 24] (* Jean-François Alcover, Dec 28 2017, after Andrew Howroyd and Wouter Meeussen *)
CROSSREFS
Row sums of A276543.
Cf. A084708.
Sequence in context: A205799 A296549 A056365 * A353016 A006400 A254342
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Apr 09 2017
STATUS
approved

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Last modified April 22 01:34 EDT 2024. Contains 371887 sequences. (Running on oeis4.)