login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A158402 a(n) = 841*n - 1. 2

%I

%S 840,1681,2522,3363,4204,5045,5886,6727,7568,8409,9250,10091,10932,

%T 11773,12614,13455,14296,15137,15978,16819,17660,18501,19342,20183,

%U 21024,21865,22706,23547,24388,25229,26070,26911,27752,28593,29434

%N a(n) = 841*n - 1.

%C The identity (841*n-1)^2 - (841*n^2-2*n)*(29)^2 = 1 can be written as a(n)^2 - A158401(n)*(29)^2 = 1.

%H Vincenzo Librandi, <a href="/A158402/b158402.txt">Table of n, a(n) for n = 1..10000</a>

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&amp;tstart=0">X^2-AY^2=1</a>

%H E. J. Barbeau, <a href="http://www.math.toronto.edu/barbeau/home.html">Polynomial Excursions</a>, Chapter 10: <a href="http://www.math.toronto.edu/barbeau/hxpol10.pdf">Diophantine equations</a> (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(29^2*t-2)).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 2*a(n-1) - a(n-2).

%F G.f.: x*(840+x)/(1-x)^2.

%t LinearRecurrence[{2,-1},{840,1681},50]

%t 841 Range[40]-1 (* _Harvey P. Dale_, Jan 29 2011 *)

%o (MAGMA) I:=[840, 1681]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

%o (PARI) a(n) = 841*n - 1.

%Y Cf. A158401.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 18 2009

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 11 01:51 EDT 2020. Contains 335600 sequences. (Running on oeis4.)