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%I #27 Sep 08 2022 08:45:42
%S 7960,15960,23960,31960,39960,47960,55960,63960,71960,79960,87960,
%T 95960,103960,111960,119960,127960,135960,143960,151960,159960,167960,
%U 175960,183960,191960,199960,207960,215960,223960,231960,239960,247960,255960
%N a(n) = 8000*n - 40.
%C The identity (80000*n^2 - 800*n + 1)^2 - (100*n^2 - n)*(8000*n - 40)^2 = 1 can be written as A157661(n)^2 - A157659(n)*a(n)^2 = 1 (see also the second part of the comment at A157661). - _Vincenzo Librandi_, Jan 28 2012
%H Vincenzo Librandi, <a href="/A157660/b157660.txt">Table of n, a(n) for n = 1..10000</a>
%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5773864&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 28 2012
%F G.f.: x*(40*x+7960)/(x-1)^2. - _Vincenzo Librandi_, Jan 28 2012
%F E.g.f.: 40*(1 - (1 - 200*x)*exp(x)). _G. C. Greubel_, Nov 17 2018
%t LinearRecurrence[{2,-1},{7960,15960},40] (* _Vincenzo Librandi_, Jan 28 2012 *)
%o (Magma) I:=[7960, 15960]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Jan 28 2012
%o (PARI) for(n=1, 40, print1(8000*n-40", ")); \\ _Vincenzo Librandi_, Jan 28 2012
%o (Sage) [40*(200*n - 1) for n in (1..40)] # _G. C. Greubel_, Nov 17 2018
%o (GAP) List([1..40], n -> 40*(200*n - 1)); # _G. C. Greubel_, Nov 17 2018
%Y Cf. A157659, A157661.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 04 2009
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