A091266 Number of orbits of length n under the map whose periodic points are counted by A061694.

0, 0, 12, 216, 3500, 58494, 1028167, 18954072, 363991752, 7231521650, 147777013109, 3091874792274, 65993049570175, 1432803420182428, 31570847522072400, 704668366087255200, 15907964778448807820

Offset

1,3

Comments

Old name was: A061694 appears to count the periodic points for a certain map. If so, then this is the sequence of the numbers of orbits of length n under that map.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..200

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, Extended Bell and Stirling Numbers From Hypergeometric Exponentiation, J. Integer Seqs. Vol. 4 (2001), #01.1.4.

Thomas Ward, Exactly realizable sequences. [local copy].

Formula

If b(n) is the n-th term of A061694, then a(n) = (1/n)*Sum_{d|n}mu(d)b(n/d).

a(n) ~ 3^(3*n + 1) / (8 * Pi^2 * n^3). - Vaclav Kotesovec, Sep 05 2019

Example

b(1)=0, b(3)=36 so a(3)=12.

Mathematica

Table[Sum[MoebiusMu[d] * Sum[Sum[((n/d)!/(i!*j!*(n/d - i - j)!))^3/6, {i, 1, n/d - j - 1}], {j, 1, n/d}], {d, Divisors[n]}]/n, {n, 1, 20}] (* Vaclav Kotesovec, Sep 05 2019 *)

Crossrefs

Cf. A061694.

Sequence in context: A274956 A116164 A268369 * A119309 A034788 A082165

Adjacent sequences: A091263 A091264 A091265 * A091267 A091268 A091269

Keyword

nonn

Author

Thomas Ward, Feb 24 2004

Extensions

Name clarified by Michel Marcus, May 14 2015

Status

approved