A060478 - OEIS

%I #18 Nov 23 2022 10:08:17

%S 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,

%T 33,270,136,0,144,18,0,0,160,0,168,0,696,96,0,48,0,3726,1752,0,208,96,

%U 1896,52,216,0,0,60,28512,1120,2208,16896,0,0,0,35904,1080,594,1112,12096

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

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

%H Manfred Einsiedler, Graham Everest and Thomas Ward, <a href="https://doi.org/10.1112/S1461157000000255">Primes in sequences associated to polynomials (after Lehmer)</a>, LMS J. Comput. Math. 3 (2000), 125-139.

%H G. Everest and T. Ward, <a href="https://ueaeprints.uea.ac.uk/id/eprint/19703">Primes in Divisibility Sequences</a>, Cubo Matematica Educacional (2001), 3 (2), pp. 245-259.

%H Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/WARD/short.html">Arithmetic and growth of periodic orbits</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

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

%o (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)));

%o id(nn) = matrix(nn, nn, n, k, n==k);

%o 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

%o a(n) = sumdiv(n, d, moebius(d)*b(n/d))/n; \\ _Michel Marcus_, Nov 23 2022

%Y Cf. A059928.

%K easy,nonn

%O 1,4

%A _Thomas Ward_

%E More terms from _T. D. Noe_, Sep 15 2003