A002823 Number of period-n solutions to a certain "universal" equation related to transformations on the unit interval.

1, 1, 3, 4, 9, 14, 27, 48, 93, 163, 315, 576, 1085

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• more

Comments

a(n) <= A000048(n), since the solutions counted here are a subset of the solutions counted by A000048 (called U sequence in the paper). The observed equality for prime n means that there are in this case no harmonics, which would disappear. - M. F. Hasler, Nov 05 2014

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• N. Metropolis, M. L. Stein and P. R. Stein, On finite limit sets for transformations on the unit interval, J. Combin. Theory, A 15 (1973), 25-44; reprinted in P. Cvitanovic, ed., Universality in Chaos, Hilger, Bristol, 1986, pp. 187-206.
• P. R. Stein, Letter to N. J. A. Sloane, Jun 02 1971

Crossrefs

Cf. A000048, A001372.