A157610 - OEIS

%I #13 Sep 08 2022 08:45:42

%S 28799,116161,262087,466577,729631,1051249,1431431,1870177,2367487,

%T 2923361,3537799,4210801,4942367,5732497,6581191,7488449,8454271,

%U 9478657,10561607,11703121,12903199,14161841,15479047,16854817,18289151

%N 29282n^2 - 484n + 1.

%C The identity (29282*n^2-484*n+1)^2-(121*n^2-2*n)*(2662*n-22)^2=1 can be written as (a(n))^2-(A157040(n))* (A157609(n)) ^2=1.

%H Vincenzo Librandi, <a href="/A157610/b157610.txt">Table of n, a(n) for n = 1..10000</a>

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5771301&amp;tstart=0">X^2-AY^2=1</a>

%H Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">Pell Equation</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).

%F G.f: x*(-28799-29764*x-x^2)/(x-1)^3.

%t LinearRecurrence[{3,-3,1},{28799,116161,262087},40]

%o (Magma) I:=[28799, 116161, 262087]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];

%o (PARI) a(n) = 29282*n^2-484*n+1.

%Y Cf. A157040, A157609.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 03 2009