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A157924 a(n) = 98*n - 1. 2

%I #22 Sep 08 2022 08:45:42

%S 97,195,293,391,489,587,685,783,881,979,1077,1175,1273,1371,1469,1567,

%T 1665,1763,1861,1959,2057,2155,2253,2351,2449,2547,2645,2743,2841,

%U 2939,3037,3135,3233,3331,3429,3527,3625,3723,3821,3919,4017,4115,4213,4311

%N a(n) = 98*n - 1.

%C The identity (98n - 1)^2 - (49n^2 - n)*14^2 = 1 can be written as a(n)^2 - A157923(n)*14^2 = 1. - _Vincenzo Librandi_, Feb 05 2012

%H Vincenzo Librandi, <a href="/A157924/b157924.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 14 in the first table at p. 85, case d(t) = t*(7^2*t-1)).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: x*(x+97)/(x-1)^2. - _Vincenzo Librandi_, Feb 05 2012

%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Feb 05 2012

%t LinearRecurrence[{2, -1}, {97, 195}, 50] (* _Vincenzo Librandi_, Feb 05 2012 *)

%t 98*Range[50]-1 (* _Harvey P. Dale_, Mar 14 2016 *)

%o (Magma) I:=[97, 195]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 05 2012

%o (PARI) for(n=1, 40, print1(98*n - 1", ")); \\ _Vincenzo Librandi_, Feb 05 2012

%Y Cf. A157923.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 09 2009

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)