%I #22 Sep 08 2022 08:45:50
%S 170,678,1524,2708,4230,6090,8288,10824,13698,16910,20460,24348,28574,
%T 33138,38040,43280,48858,54774,61028,67620,74550,81818,89424,97368,
%U 105650,114270,123228,132524,142158,152130,162440,173088,184074,195398,207060,219060,231398,244074,257088,270440,284130,298158,312524
%N a(n) = 169*n^2 + n.
%C The identity (338*n + 1)^2 - (169*n^2 + n)*26^2 = 1 can be written as A158000(n)^2 - a(n)*26^2 = 1. - _Vincenzo Librandi_, Feb 10 2012
%H Vincenzo Librandi, <a href="/A173275/b173275.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*(13^2*t+1)).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: x*(-170 - 168*x)/(x-1)^3. - _Vincenzo Librandi_, Feb 10 2012
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Feb 10 2012
%t LinearRecurrence[{3, -3, 1}, {170, 678, 1524}, 50] (* _Vincenzo Librandi_, Feb 10 2012 *)
%o (Magma)[169*n^2+n: n in [1..50]]
%o (PARI) for(n=1, 50, print1(169*n^2+n ", ")); \\ _Vincenzo Librandi_, Feb 10 2012
%Y Cf. A031704, A158000.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Nov 22 2010