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

%I A020729 #54 Dec 06 2024 15:44:26
%S A020729 2,10,50,250,1250,6250,31250,156250,781250,3906250,19531250,97656250,
%T A020729 488281250,2441406250,12207031250,61035156250,305175781250,
%U A020729 1525878906250,7629394531250,38146972656250,190734863281250,953674316406250,4768371582031250,23841857910156250
%N A020729 Pisot sequences E(2,10), L(2,10), P(2,10), T(2,10).
%H A020729 Vincenzo Librandi, <a href="/A020729/b020729.txt">Table of n, a(n) for n = 0..1000</a>
%H A020729 Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger, <a href="https://arxiv.org/abs/1609.05570">Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences</a>, arXiv preprint, arXiv:1609.05570 [math.NT], 2016.
%H A020729 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A020729 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (5).
%F A020729 a(n) = 2*5^n.
%F A020729 a(n) = 5*a(n-1).
%F A020729 G.f.: 2/(1-5*x). - _Philippe Deléham_, Nov 23 2008
%F A020729 From _Amiram Eldar_, May 08 2023: (Start)
%F A020729 Sum_{n>=0} 1/a(n) = 5/8.
%F A020729 Sum_{n>=0} (-1)^n/a(n) = 5/12.
%F A020729 Product_{n>=0} (1 - 1/a(n)) = A132021. (End)
%F A020729 From _Elmo R. Oliveira_, Dec 06 2024: (Start)
%F A020729 E.g.f.: 2*exp(5*x).
%F A020729 a(n) = 2*A000351(n). (End)
%t A020729 Join[{a=2}, Table[a=5*a, {n, 0, 60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 09 2011 *)
%t A020729 Join[{2},NestList[5#&,10,30]] (* _Harvey P. Dale_, Jan 19 2013 *)
%o A020729 (Magma) [2*5^n: n in [0..25]]; // _Vincenzo Librandi_, Sep 15 2011
%Y A020729 Essentially a duplicate of A020699.
%Y A020729 See A008776 for definitions of Pisot sequences.
%Y A020729 Cf. A000351, A132021.
%K A020729 nonn,easy
%O A020729 0,1
%A A020729 _David W. Wilson_