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a(n) = 196*n^2 - n.
2

%I #23 Feb 27 2024 11:58:59

%S 195,782,1761,3132,4895,7050,9597,12536,15867,19590,23705,28212,33111,

%T 38402,44085,50160,56627,63486,70737,78380,86415,94842,103661,112872,

%U 122475,132470,142857,153636,164807,176370,188325,200672,213411,226542

%N a(n) = 196*n^2 - n.

%C The identity (392*n - 1)^2 - (196*n^2 - n)*28^2 = 1 can be written as A158004(n)^2 - a(n)*28^2 = 1. - _Vincenzo Librandi_, Feb 10 2012

%H Vincenzo Librandi, <a href="/A158003/b158003.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*(14^2*t-1)).

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

%F G.f.: x*(-195 - 197*x)/(x-1)^3. - _Vincenzo Librandi_, Feb 10 2012

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Feb 10 2012

%t LinearRecurrence[{3, -3, 1}, {195, 782, 1761}, 50] (* _Vincenzo Librandi_, Feb 10 2012 *)

%o (Magma) I:=[195, 782, 1761]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Feb 10 2012

%o (PARI) for(n=1, 50, print1(196*n^2 - n", ")); \\ _Vincenzo Librandi_, Feb 10 2012

%Y Cf. A158004.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 11 2009