A157510 - OEIS

%I #21 Oct 05 2024 20:56:19

%S 1020,2020,3020,4020,5020,6020,7020,8020,9020,10020,11020,12020,13020,

%T 14020,15020,16020,17020,18020,19020,20020,21020,22020,23020,24020,

%U 25020,26020,27020,28020,29020,30020,31020,32020,33020,34020,35020

%N a(n) = 1000*n + 20.

%C The identity (5000*n^2 + 200*n + 1)^2 - (25*n^2 + n)*(1000*n + 20)^2 = 1 can be written as A157511(n)^2 - A173089(n)*a(n)^2 = 1 (see also second part of the comment at A173089). - _Vincenzo Librandi_, Feb 04 2012

%H Vincenzo Librandi, <a href="/A157510/b157510.txt">Table of n, a(n) for n = 1..10000</a>

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5771301&amp;tstart=0">X^2-AY^2=1</a>

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

%F G.f.: x*(1020-20*x)/(1-x)^2. - _Vincenzo Librandi_, Feb 04 2012

%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Feb 04 2012

%t LinearRecurrence[{2, -1}, {1020, 2020}, 50] (* _Vincenzo Librandi_, Feb 04 2012 *)

%o (Magma) I:=[1020, 2020]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 04 2012

%o (PARI) for(n=1, 40, print1(1000*n + 20", ")); \\ _Vincenzo Librandi_, Feb 04 2012

%Y Cf. A157511, A173089.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 02 2009