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 A158364 529n^2 - 2n. 2

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

%S 527,2112,4755,8456,13215,19032,25907,33840,42831,52880,63987,76152,

%T 89375,103656,118995,135392,152847,171360,190931,211560,233247,255992,

%U 279795,304656,330575,357552,385587,414680,444831,476040,508307,541632

%N 529n^2 - 2n.

%C The identity (529*n-1)^2-(529*n^2-2*n)*(23)^2=1 can be written as A158365(n)^2-a(n)*(23)^2=1.

%H Vincenzo Librandi, <a href="/A158364/b158364.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*(-527-531*x)/(x-1)^3.

%t LinearRecurrence[{3,-3,1},{527,2112,4755},50]

%o (Magma) I:=[527, 2112, 4755]; [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. A158365.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 17 2009

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Last modified September 7 05:42 EDT 2024. Contains 375729 sequences. (Running on oeis4.)