A158367 - OEIS

%I #19 Sep 08 2022 08:45:43

%S 531,2120,4767,8472,13235,19056,25935,33872,42867,52920,64031,76200,

%T 89427,103712,119055,135456,152915,171432,191007,211640,233331,256080,

%U 279887,304752,330675,357656,385695,414792,444947,476160,508431,541760

%N 529n^2 + 2n.

%C The identity (529*n+1)^2-(529*n^2+2*n)*(23)^2=1 can be written as A158368(n)^2-a(n)*(23)^2=1.

%H Vincenzo Librandi, <a href="/A158367/b158367.txt">Table of n, a(n) for n = 1..10000</a>

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&amp;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 15 in the first table at p. 85, case d(t) = t*(23^2*t+2)).

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

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

%F G.f.: x*(531+527*x)/(1-x)^3.

%t LinearRecurrence[{3,-3,1},{531,2120,4767},50]

%o (Magma) I:=[531, 2120, 4767]; [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) = 529*n^2 + 2*n.

%Y Cf. A158368.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 17 2009