A091268 Number of orbits of length n under the map whose periodic points are counted by A061685.

1, 4, 99, 6272, 876725, 232419936, 105471170140, 76095730062464, 82555139387847312, 128928209221144677400, 279860608037771819829980, 820360089598849358326307904, 3169977309466844379463315722484

Offset: 1

Author

Thomas Ward, Feb 24 2004

Keywords

• nonn

Comments

Old name was: A061685 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 for that map.

Examples

			b(1)=1, b(2)=9, b(3)=298. Hence a(3)=(1/3)(b(3)-b(1))=99.
		

Links

• 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. A061685.

Formula

If b(n) is the (n+1)th term of A061685, then a(n) = (1/n)*Sum_{d|n}mu(d)b(n/d).

Extensions

Name clarified by Michel Marcus, May 14 2015