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

Author

Andrew Howroyd, Apr 09 2017

Keywords

• nonn

Links

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

Crossrefs

Row sums of A276544.

Cf. A103293.

Programs

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 *)

Formula

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