A158403 - OEIS

%I #17 Sep 08 2022 08:45:43

%S 843,3368,7575,13464,21035,30288,41223,53840,68139,84120,101783,

%T 121128,142155,164864,189255,215328,243083,272520,303639,336440,

%U 370923,407088,444935,484464,525675,568568,613143,659400,707339,756960,808263,861248

%N 841n^2 + 2n.

%C The identity (841*n+1)^2-(841*n^2+2*n)*29^2=1 can be written as A158404(n)^2-a(n)*29^2=1.

%H Vincenzo Librandi, <a href="/A158403/b158403.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 15 in the first table at p. 85, case d(t) = t*(29^2*t+2)).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: x*(843+839*x)/(1-x)^3.

%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).

%t LinearRecurrence[{3,-3,1},{843,3368,7575},50]

%o (Magma) I:=[843, 3368, 7575]; [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) = 841*n^2 + 2*n.

%Y Cf. A158404.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 18 2009