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A158373 625n^2 - 2n. 2

%I #15 Sep 08 2022 08:45:43

%S 623,2496,5619,9992,15615,22488,30611,39984,50607,62480,75603,89976,

%T 105599,122472,140595,159968,180591,202464,225587,249960,275583,

%U 302456,330579,359952,390575,422448,455571,489944,525567,562440,600563,639936

%N 625n^2 - 2n.

%C The identity (625*n-1)^2-(625*n^2-2*n)*(25)^2=1 can be written as A158374(n)^2-a(n)*(25)^2=1.

%H Vincenzo Librandi, <a href="/A158373/b158373.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*(25^2*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*(-623-627*x)/(x-1)^3.

%t LinearRecurrence[{3,-3,1},{623,2496,5619},50]

%o (Magma) I:=[623, 2496, 5619]; [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) = 625*n^2 - 2*n.

%Y Cf. A158374.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 17 2009

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)