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A158394 729n^2 - 2n. 2

%I

%S 727,2912,6555,11656,18215,26232,35707,46640,59031,72880,88187,104952,

%T 123175,142856,163995,186592,210647,236160,263131,291560,321447,

%U 352792,385595,419856,455575,492752,531387,571480,613031,656040,700507,746432

%N 729n^2 - 2n.

%C The identity (729*n-1)^2-(729*n^2-2*n)*(27)^2=1 can be written as A158395(n)^2-a(n)*(27)^2=1.

%H Vincenzo Librandi, <a href="/A158394/b158394.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*(27^2*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*(-727-731*x)/(x-1)^3.

%t LinearRecurrence[{3,-3,1},{727,2912,6555},50]

%o (MAGMA) I:=[727, 2912, 6555]; [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) = 729*n^2 - 2*n.

%Y Cf. A158395.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 18 2009

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Last modified February 27 07:05 EST 2020. Contains 332299 sequences. (Running on oeis4.)