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

Author

Thomas Ward, Feb 24 2004

Keywords

• nonn

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.

Examples

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

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].

Crossrefs

Cf. A061694.

Programs

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 *)

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

Extensions

Name clarified by Michel Marcus, May 14 2015