A276549 Number of primitive (aperiodic) reversible string structures with n beads using an infinite alphabet.

1, 1, 3, 9, 31, 112, 467, 2141, 10739, 58454, 340389, 2110093, 13830234, 95475087, 691543059, 5240282987, 41432986587, 341040306207, 2916376237349, 25862097428262, 237434959190586, 2253358056942644, 22076003468637449, 222979436688500085, 2319295172178428701

Offset

1,3

Links

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

Formula

a(n) = Sum_{d|n} mu(n/d) * A103293(d+1).

Mathematica

b[n_] := SeriesCoefficient[Exp[(Exp[2*x] - 3)/2 + Exp[x]], {x, 0, n}]*n!;
c[n_] := If[n == 0, 1, (BellB[n - 1] + If[Mod[n, 2] == 1, b[(n - 1)/2], Sum[Binomial[n/2 - 1, k]*b[k], {k, 0, n/2 - 1}]])/2];
a[n_] := DivisorSum[n, MoebiusMu[n/#] c[# + 1]&];
Array[a, 25] (* Jean-François Alcover, Jun 16 2017, using Alois P. Heinz's code for A103293 *)

Crossrefs

Row sums of A276544.

Cf. A103293.

Sequence in context: A056334 A063032 A056335 * A049188 A049165 A052709

Adjacent sequences: A276546 A276547 A276548 * A276550 A276551 A276552

Keyword

nonn

Author

Andrew Howroyd, Apr 09 2017

Status

approved