|
%I #21 Sep 08 2022 08:45:42
%S 980,1980,2980,3980,4980,5980,6980,7980,8980,9980,10980,11980,12980,
%T 13980,14980,15980,16980,17980,18980,19980,20980,21980,22980,23980,
%U 24980,25980,26980,27980,28980,29980,30980,31980,32980,33980,34980
%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 A157516(n)^2 - A157514(n)*a(n)^2 = 1 (see also the second part of the comment at A157514). - _Vincenzo Librandi_, Jan 26 2012
%H Vincenzo Librandi, <a href="/A157515/b157515.txt">Table of n, a(n) for n = 1..10000</a>
%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5771301&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 a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Jan 26 2012
%F G.f.: x*(980 + 20*x)/(1-x)^2. - _Vincenzo Librandi_, Jan 26 2012
%t LinearRecurrence[{2,-1},{980,1980},50] (* _Vincenzo Librandi_, Jan 26 2012 *)
%o (Magma) I:=[980, 1980]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Jan 26 2012
%o (PARI) for(n=1, 22, print1(1000*n - 20", ")); \\ _Vincenzo Librandi_, Jan 26 2012
%Y Cf. A157514, A157516.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 02 2009
|
