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A157441 a(n) = 1331*n - 1122.

%I A157441 #18 Sep 08 2022 08:45:42
%S A157441 209,1540,2871,4202,5533,6864,8195,9526,10857,12188,13519,14850,16181,
%T A157441 17512,18843,20174,21505,22836,24167,25498,26829,28160,29491,30822,
%U A157441 32153,33484,34815,36146,37477,38808,40139,41470,42801,44132,45463
%N A157441 a(n) = 1331*n - 1122.
%C A157441 The identity (14641*n^2 - 24684*n + 10405)^2 - (121*n^2 - 204*n + 86)*(1331*n - 1122)^2 = 1 can be written as A157442(n)^2 - A157440(n)*a(n)^2 = 1. - _Vincenzo Librandi_, Jan 29 2012
%H A157441 Vincenzo Librandi, <a href="/A157441/b157441.txt">Table of n, a(n) for n = 1..10000</a>
%H A157441 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&amp;tstart=0">X^2-AY^2=1</a>
%H A157441 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A157441 G.f.: x*(209 + 1122*x)/(x-1)^2. - _Vincenzo Librandi_, Jan 29 2012
%F A157441 a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Jan 29 2012
%t A157441 LinearRecurrence[{2,-1},{209,1540},50] (* _Vincenzo Librandi_, Jan 29 2012 *)
%o A157441 (Magma) I:=[209, 1540]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Jan 29 2012
%o A157441 (PARI) for(n=1, 40, print1(1331*n - 1122", ")); \\ _Vincenzo Librandi_, Jan 29 2012
%Y A157441 Cf. A157440, A157442.
%K A157441 nonn,easy
%O A157441 1,1
%A A157441 _Vincenzo Librandi_, Mar 01 2009