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