A060478 Number of orbits of length n in map whose periodic points are A059928.

1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 12, 56, 0, 0, 0, 72, 0, 0, 24, 0, 0, 96, 24, 0, 48, 0, 0, 33, 270, 136, 0, 144, 18, 0, 0, 160, 0, 168, 0, 696, 96, 0, 48, 0, 3726, 1752, 0, 208, 96, 1896, 52, 216, 0, 0, 60, 28512, 1120, 2208, 16896, 0, 0, 0, 35904, 1080, 594, 1112, 12096

Offset

1,4

References

G. Everest and T. Ward, Heights of Polynomials and Entropy in Algebraic Dynamics, Springer, London, 1999.

Links

Table of n, a(n) for n=1..70.

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

G. Everest and T. Ward, Primes in Divisibility Sequences, Cubo Matematica Educacional (2001), 3 (2), pp. 245-259.

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

Formula

a(n) = (1/n) * Sum_{ d divides n } mu(d) * A059928(n/d).

Prog

(PARI) comp(pol) = my(v=Vec(pol), nn=poldegree(pol)); matrix(nn, nn, n, k, if (k==nn, -v[n], if(k==n-1, 1)));
id(nn) = matrix(nn, nn, n, k, n==k);
b(n) = my(p=x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1, m=comp(p)); abs(matdet(m^n-id(poldegree(p)))); \\ A059928
a(n) = sumdiv(n, d, moebius(d)*b(n/d))/n; \\ Michel Marcus, Nov 23 2022

Crossrefs

Cf. A059928.

Sequence in context: A122698 A002483 A282530 * A088806 A359602 A280618

Adjacent sequences: A060475 A060476 A060477 * A060479 A060480 A060481

Keyword

easy,nonn

Author

Thomas Ward

Extensions

More terms from T. D. Noe, Sep 15 2003

Status

approved