A158420 - OEIS

%I #15 Sep 08 2022 08:45:43

%S 1022,4092,9210,16376,25590,36852,50162,65520,82926,102380,123882,

%T 147432,173030,200676,230370,262112,295902,331740,369626,409560,

%U 451542,495572,541650,589776,639950,692172,746442,802760,861126,921540,984002

%N 1024n^2 - 2n.

%C The identity (1024*n-1)^2-(1024*n^2-2*n)*(32)^2=1 can be written as A158421(n)^2-a(n)*(32)^2=1.

%H Vincenzo Librandi, <a href="/A158420/b158420.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 E. J. Barbeau, <a href="http://www.math.toronto.edu/barbeau/home.html">Polynomial Excursions</a>, Chapter 10: <a href="http://www.math.toronto.edu/barbeau/hxpol10.pdf">Diophantine equations</a> (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(32^2*t-2)).

%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*(-1022-1026*x)/(x-1)^3.

%t LinearRecurrence[{3,-3,1},{1022,4092,9210},50]

%o (Magma) I:=[1022, 4092, 9210]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];

%o (PARI) a(n) = 1024*n^2 - 2*n.

%Y Cf. A158421.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 18 2009