A060219 Number of orbits of length n under the full 16-shift (whose periodic points are counted by A001025).

16, 120, 1360, 16320, 209712, 2795480, 38347920, 536862720, 7635496960, 109951057896, 1599289640400, 23456246655680, 346430740566960, 5146970983535160, 76861433640386288, 1152921504338411520

Offset

1,1

Comments

Number of monic irreducible polynomials of degree n over GF(16). - Robert Israel, Jan 07 2015

Number of Lyndon words (aperiodic necklaces) with n beads of 16 colors. - Andrew Howroyd, Dec 10 2017

Links

Table of n, a(n) for n=1..16.

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

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

T. Ward, Exactly realizable sequences

Formula

a(n) = (1/n)* Sum_{d|n} mu(d)*16^(n/d).

G.f.: Sum_{k>=1} mu(k)*log(1/(1 - 16*x^k))/k. - Ilya Gutkovskiy, May 19 2019

Example

a(2)=120 since there are 256 points of period 2 in the full 16-shift and 16 fixed points, so there must be (256-16)/2 = 120 orbits of length 2.

Maple

f:= (n, p) -> add(numtheory:-mobius(d)*p^(n/d), d=numtheory:-divisors(n))/n:
seq(f(n, 16), n=1..30); # Robert Israel, Jan 07 2015

Prog

(PARI) a(n) = sumdiv(n, d, moebius(d)*16^(n/d))/n; \\ Michel Marcus, Jan 07 2015

Crossrefs

Column 16 of A074650.

Cf. A001025.

Sequence in context: A164542 A351383 A027049 * A185760 A301649 A014732

Adjacent sequences: A060216 A060217 A060218 * A060220 A060221 A060222

Keyword

easy,nonn

Author

Thomas Ward, Mar 21 2001

Status

approved