A157821 - OEIS

%I #15 Sep 08 2022 08:45:42

%S 8984580,17968830,26953080,35937330,44921580,53905830,62890080,

%T 71874330,80858580,89842830,98827080,107811330,116795580,125779830,

%U 134764080,143748330,152732580,161716830,170701080,179685330,188669580,197653830

%N 8984250n + 330.

%C The identity (1482401250*n^2+108900*n+1)^2-(27225*n^2+2*n)*(8984250*n+330)^2=1 can be written as A157822(n)^2-A157820(n)*a(n)^2=1.

%H Vincenzo Librandi, <a href="/A157821/b157821.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*(8984580-330x)/(1-x)^2.

%t LinearRecurrence[{2,-1},{8984580,17968830},30]

%o (Magma) I:=[8984580, 17968830]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..30]];

%o (PARI) a(n) = 8984250*n + 330.

%Y Cf. A157820, A157822.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 07 2009