A020729 Pisot sequences E(2,10), L(2,10), P(2,10), T(2,10).

2, 10, 50, 250, 1250, 6250, 31250, 156250, 781250, 3906250, 19531250, 97656250, 488281250, 2441406250, 12207031250, 61035156250, 305175781250, 1525878906250, 7629394531250, 38146972656250, 190734863281250, 953674316406250, 4768371582031250, 23841857910156250

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences, arXiv preprint, arXiv:1609.05570 [math.NT], 2016.

Tanya Khovanova, Recursive Sequences.

Index entries for linear recurrences with constant coefficients, signature (5).

Formula

a(n) = 2*5^n.

a(n) = 5*a(n-1).

G.f.: 2/(1-5*x). - Philippe Deléham, Nov 23 2008

From Amiram Eldar, May 08 2023: (Start)

Sum_{n>=0} 1/a(n) = 5/8.

Sum_{n>=0} (-1)^n/a(n) = 5/12.

Product_{n>=0} (1 - 1/a(n)) = A132021. (End)

From Elmo R. Oliveira, Dec 06 2024: (Start)

E.g.f.: 2*exp(5*x).

a(n) = 2*A000351(n). (End)

Mathematica

Join[{a=2}, Table[a=5*a, {n, 0, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)
Join[{2}, NestList[5#&, 10, 30]] (* Harvey P. Dale, Jan 19 2013 *)

Prog

(Magma) [2*5^n: n in [0..25]]; // Vincenzo Librandi, Sep 15 2011

Crossrefs

Essentially a duplicate of A020699.

See A008776 for definitions of Pisot sequences.

Cf. A000351, A132021.

Sequence in context: A015954 A015949 A020699 * A110170 A026332 A027908

Adjacent sequences: A020726 A020727 A020728 * A020730 A020731 A020732

Keyword

nonn,easy

Author

David W. Wilson

Status

approved