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A157444 a(n) = 1331*n - 209. 3

%I #18 Sep 08 2022 08:45:42

%S 1122,2453,3784,5115,6446,7777,9108,10439,11770,13101,14432,15763,

%T 17094,18425,19756,21087,22418,23749,25080,26411,27742,29073,30404,

%U 31735,33066,34397,35728,37059,38390,39721,41052,42383,43714,45045,46376

%N a(n) = 1331*n - 209.

%C The identity (14641*n^2 - 4598*n + 362)^2 - (121*n^2 - 38*n + 3)*(1331*n - 209)^2 = 1 can be written as A157445(n)^2 - A157443(n)*a(n)^2 = 1. - _Vincenzo Librandi_, Jan 26 2012

%H Vincenzo Librandi, <a href="/A157444/b157444.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 <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*(209*x + 1122)/(x-1)^2. - _Vincenzo Librandi_, Jan 26 2012

%t LinearRecurrence[{2,-1},{1122,2453},40] (* _Vincenzo Librandi_, Jan 26 2012 *)

%o (Magma) I:=[1122, 2453]; [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(1331*n - 209", ")); \\ _Vincenzo Librandi_, Jan 26 2012

%Y Cf. A157443, A157445.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 01 2009

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Last modified March 29 05:28 EDT 2024. Contains 371264 sequences. (Running on oeis4.)