A060169 Number of orbits of length n under the automorphism of the 3-torus whose periodic points are counted by A001945.

1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 2, 2, 2, 4, 4, 5, 8, 6, 12, 13, 16, 23, 26, 35, 46, 54, 76, 89, 120, 154, 192, 255, 322, 411, 544, 679, 898, 1145, 1476, 1925, 2466, 3201, 4156, 5338, 6978, 8985

Offset

1,9

Comments

The sequence A001945 records the number of points of period n under a map. The number of orbits of length n for this map gives the sequence above.

Links

Table of n, a(n) for n=1..46.

Manfred Einsiedler, Graham Everest and Thomas Ward, Primes in sequences associated to polynomials (after Lehmer), LMS J. Comput. Math. 3 (2000), 125-139.

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

Yash Puri and Thomas Ward, A dynamical property unique to the Lucas sequence, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402.

Formula

a(n) = (1/n)* Sum_{ d divides n } mu(d)*A001945(n/d).

Example

u(17) = 8 since the map whose periodic points are counted by A001945 has 1 fixed point and 137 points of period 17, hence 8 orbits of length 7.

Crossrefs

Cf. A001642, A060164, A060165, A060166, A060167, A060168, A060170, A060171, A060171, A060172, A060173.

Sequence in context: A009213 A072209 A226559 * A117958 A113401 A071227

Adjacent sequences: A060166 A060167 A060168 * A060170 A060171 A060172

Keyword

easy,nonn

Author

Thomas Ward, Mar 13 2001

Status

approved