|
%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&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
|
