A157949 - OEIS

%I #33 Feb 08 2022 02:47:25

%S 127,255,383,511,639,767,895,1023,1151,1279,1407,1535,1663,1791,1919,

%T 2047,2175,2303,2431,2559,2687,2815,2943,3071,3199,3327,3455,3583,

%U 3711,3839,3967,4095,4223,4351,4479,4607,4735,4863,4991,5119,5247,5375,5503

%N a(n) = 128*n - 1.

%C The identity (128*n-1)^2 - (64*n^2-n)*(16)^2 = 1 can be written as a(n)^2 - A157948(n)*(16)^2 = 1. - _Vincenzo Librandi_, Jan 29 2012

%H Vincenzo Librandi, <a href="/A157949/b157949.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*(8^2*t-1)).

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&amp;tstart=0">X^2-AY^2=1</a> [broken link]

%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). - _Vincenzo Librandi_, Jan 29 2012

%F G.f.: x*(127+x)/(1-x)^2. - _Vincenzo Librandi_, Jan 29 2012

%o (PARI) for(n=1, 40, print1(128*n - 1", ")); \\ _Vincenzo Librandi_, Jan 29 2012

%Y Cf. A157948.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 10 2009