A157843 - OEIS

%I #16 Sep 08 2022 08:45:42

%S 384240,2112240,3840240,5568240,7296240,9024240,10752240,12480240,

%T 14208240,15936240,17664240,19392240,21120240,22848240,24576240,

%U 26304240,28032240,29760240,31488240,33216240,34944240,36672240

%N 1728000n - 1343760.

%C The identity (103680000*n^2-161251200*n+62697601)^2-(3600*n^2-5599*n+2177)*(1728000*n-1343760)^2=1 can be written as A157844(n)^2-A157842(n)*a(n)^2=1.

%H Vincenzo Librandi, <a href="/A157843/b157843.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*(384240+1343760*x)/(x-1)^2.

%t LinearRecurrence[{2,-1},{384240,2112240},40]

%o (Magma) I:=[384240, 2112240]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

%o (PARI) a(n) = 1728000*n - 1343760.

%Y Cf. A157842, A157844.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 07 2009