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A091268 Number of orbits of length n under the map whose periodic points are counted by A061685. 0
1, 4, 99, 6272, 876725, 232419936, 105471170140, 76095730062464, 82555139387847312, 128928209221144677400, 279860608037771819829980, 820360089598849358326307904, 3169977309466844379463315722484 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..13.

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

EXAMPLE

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

CROSSREFS

Cf. A061685.

Sequence in context: A180830 A265721 A224475 * A326085 A158082 A017090

Adjacent sequences:  A091265 A091266 A091267 * A091269 A091270 A091271

KEYWORD

nonn

AUTHOR

Thomas Ward (t.ward(AT)uea.ac.uk), Feb 24 2004

EXTENSIONS

Name clarified by Michel Marcus, May 14 2015

STATUS

approved

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Last modified January 28 03:42 EST 2020. Contains 331317 sequences. (Running on oeis4.)