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

Author

Thomas Ward

Keywords

• easy
• nonn

References

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

Links

• 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.

Crossrefs

Cf. A059928.

Programs

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

Formula

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

Extensions

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