A112639 a(n) = floor(r^n) where r is the smallest Pisot number (real root r=1.3247179... of x^3-x-1).

1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 22, 29, 38, 51, 67, 89, 119, 157, 209, 276, 366, 486, 643, 853, 1130, 1496, 1983, 2626, 3480, 4610, 6106, 8090, 10716, 14196, 18807, 24913, 33004, 43721, 57917, 76725, 101638, 134643, 178364, 236281, 313007, 414645

Offset: 0

Author

Roger L. Bagula, Mar 31 2006

Keywords

• nonn

Links

• Andrei Vieru, Pisot Numbers and Primes, arXiv:1205.1054 [math.NT], Apr 04 2012.

Crossrefs

Cf. A060006 (decimal expansion of r=1.32471795724475...).

Cf. A051016, A051017.

Cf. A205579 (definition using round() instead of floor()).

Programs

Mathematica

r = Solve[x^3 - x - 1 == 0, x][[1,1,2]]; Table[Floor[r^n], {n, 0, 50}] (* T. D. Noe, Jan 30 2012 *)

PARI

default(realprecision,110);
default(format,"g.15");
r=real(polroots(x^3-x-1)[1])
v=vector(66, n, floor(r^(n-1)) )  /* Joerg Arndt, Jan 29 2012 */

Formula

a(n) = floor(((1/2+sqrt(23/108))^(1/3) + (1/2-sqrt(23/108))^(1/3))^n). - Jwalin Bhatt, May 06 2025

Extensions

Completely edited by Joerg Arndt, Jan 29 2012