A157263 - OEIS

%I #22 Sep 08 2022 08:45:41

%S 408,2136,3864,5592,7320,9048,10776,12504,14232,15960,17688,19416,

%T 21144,22872,24600,26328,28056,29784,31512,33240,34968,36696,38424,

%U 40152,41880,43608,45336,47064,48792,50520,52248,53976,55704,57432,59160

%N a(n) = 1728*n - 1320.

%C The identity (10368*n^2-15840*n+6049)^2-(36*n^2-55*n+21)*(1728*n-1320)^2=1 can be written as A157264(n)^2-A157262(n)*a(n)^2=1. - _Vincenzo Librandi_, Jan 27 2012

%H Vincenzo Librandi, <a href="/A157263/b157263.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 27 2012

%F G.f.: x*(408+1320*x)/(x-1)^2. - _Vincenzo Librandi_, Jan 27 2012

%F E.g.f.: (1728*x - 1320)*exp(x) + 1320. - _G. C. Greubel_, Feb 04 2018

%t LinearRecurrence[{2,-1},{408,2136},40] (* _Vincenzo Librandi_, Jan 27 2012 *)

%t 1728*Range[40]-1320 (* _Harvey P. Dale_, Aug 09 2012 *)

%o (Magma) I:=[408, 2136]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Jan 27 2012

%o (PARI) for(n=1, 40, print1(1728*n - 1320", ")); \\ _Vincenzo Librandi_, Jan 27 2012

%Y Cf. A157262, A157264.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Feb 26 2009