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Pisot sequences E(2,10), L(2,10), P(2,10), T(2,10).
6

%I #50 Mar 27 2024 15:41:39

%S 2,10,50,250,1250,6250,31250,156250,781250,3906250,19531250,97656250,

%T 488281250,2441406250,12207031250,61035156250,305175781250,

%U 1525878906250,7629394531250,38146972656250,190734863281250,953674316406250,4768371582031250,23841857910156250

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

%H Vincenzo Librandi, <a href="/A020729/b020729.txt">Table of n, a(n) for n = 0..1000</a>

%H 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 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (5).

%F a(n) = 2*5^n.

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

%F G.f.: 2/(1-5*x). - _Philippe Deléham_, Nov 23 2008

%F From _Amiram Eldar_, May 08 2023: (Start)

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

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

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

%t Join[{a=2}, Table[a=5*a, {n, 0, 60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 09 2011 *)

%t Join[{2},NestList[5#&,10,30]] (* _Harvey P. Dale_, Jan 19 2013 *)

%o (Magma) [2*5^n: n in [0..25]]; // _Vincenzo Librandi_, Sep 15 2011

%Y Essentially a duplicate of A020699.

%Y See A008776 for definitions of Pisot sequences.

%Y Cf. A132021.

%K nonn,easy

%O 0,1

%A _David W. Wilson_