A157787 - OEIS

%I #21 Sep 08 2022 08:45:42

%S 6468330,15452580,24436830,33421080,42405330,51389580,60373830,

%T 69358080,78342330,87326580,96310830,105295080,114279330,123263580,

%U 132247830,141232080,150216330,159200580,168184830,177169080,186153330,195137580

%N 8984250n - 2515920.

%C The identity (1482401250*n^2-830253600*n +116250751)^2-(27225*n^2-15248*n +2135) *(8984250*n -2515920)^2=1 can be written as A157788(n)^2-A157786(n)*a(n)^2=1.

%H Vincenzo Librandi, <a href="/A157787/b157787.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).

%F G.f: x*(6468330+2515920*x)/(x-1)^2.

%t Table[8984250n-2515920,{n,30}].

%t LinearRecurrence[{2,-1},{6468330,15452580},30] (* _Harvey P. Dale_, Mar 29 2015 *)

%o (Magma) I:=[6468330, 15452580]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..30]];

%o (PARI) a(n) = 8984250*n - 2515920.

%Y Cf. A157786, A157788.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 06 2009