A276548 Number of primitive (period n) bracelet structures using an infinite alphabet.

1, 1, 2, 5, 11, 33, 92, 347, 1347, 6338, 31949, 179265, 1071264, 6845487, 46162569, 327731596, 2437753739, 18948597836, 153498350744, 1293123237572, 11306475314372, 102425554267565, 959826755336241, 9290811905211847

Offset

1,3

Links

Table of n, a(n) for n=1..24.

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

Adjacent sequences: A276545 A276546 A276547 * A276549 A276550 A276551

Keyword

nonn

Author

Andrew Howroyd, Apr 09 2017

Status

approved