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A060478
Number of orbits of length n in map whose periodic points are A059928.
1
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
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
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
More terms from T. D. Noe, Sep 15 2003
STATUS
approved