A157990 - OEIS

%I #20 Sep 08 2022 08:45:42

%S 289,577,865,1153,1441,1729,2017,2305,2593,2881,3169,3457,3745,4033,

%T 4321,4609,4897,5185,5473,5761,6049,6337,6625,6913,7201,7489,7777,

%U 8065,8353,8641,8929,9217,9505,9793,10081,10369,10657,10945,11233,11521

%N a(n) = 288*n + 1.

%C The identity (288*n + 1)^2 - (144*n^2 + n)*24^2 = 1 can be written as a(n)^2 - (A017522(n) + n)*24^2 = 1. - _Vincenzo Librandi_, Feb 10 2012

%H Vincenzo Librandi, <a href="/A157990/b157990.txt">Table of n, a(n) for n = 1..10000</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 14 in the first table at p. 85, case d(t) = t*(12^2*t+1)).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: x*(289-x)/(1-x)^2. - _Vincenzo Librandi_, Feb 10 2012

%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Feb 10 2012

%t LinearRecurrence[{2, -1}, {289, 577}, 50] (* _Vincenzo Librandi_, Feb 10 2012 *)

%o (Magma) I:=[289, 577]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 10 2012

%o (PARI) for(n=1, 50, print1(288*n + 1", ")); \\ _Vincenzo Librandi_, Feb 10 2012

%Y Cf. A017522.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 10 2009