|
%I #21 May 12 2023 15:05:14
%S 337,675,1013,1351,1689,2027,2365,2703,3041,3379,3717,4055,4393,4731,
%T 5069,5407,5745,6083,6421,6759,7097,7435,7773,8111,8449,8787,9125,
%U 9463,9801,10139,10477,10815,11153,11491,11829,12167,12505,12843,13181,13519
%N a(n) = 338n - 1.
%C The identity (338*n-1)^2-(169*n^2-n)*(26)^2=1 can be written as a(n)^2-A157998(n)*(26)^2 = 1.
%H Vincenzo Librandi, <a href="/A157999/b157999.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 14 in the first table at p. 85, case d(t) = t*(13^2*t-1)).
%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).
%F G.f.: x*(337+x)/(1-x)^2.
%t LinearRecurrence[{2,-1},{337,675},50]
%t 338*Range[40]-1 (* _Harvey P. Dale_, Jun 04 2019 *)
%o (Magma) I:=[337, 675]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
%o (PARI) a(n) = 338*n - 1.
%Y Cf. A157998.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 11 2009
|
