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A157923 49n^2 - n. 2

%I

%S 48,194,438,780,1220,1758,2394,3128,3960,4890,5918,7044,8268,9590,

%T 11010,12528,14144,15858,17670,19580,21588,23694,25898,28200,30600,

%U 33098,35694,38388,41180,44070,47058,50144,53328,56610,59990,63468,67044

%N 49n^2 - n.

%C The identity (98n-1)^2-(49n^2-n)*14^2=1 can be written as A157924(n)^2-a(n)*14^2=1. - Vincenzo Librandi, Feb 05 2012

%H Vincenzo Librandi, <a href="/A157923/b157923.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">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: x*(-48-50*x)/(x-1)^3. - Vincenzo Librandi, Feb 05 2012

%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Feb 05 2012

%t LinearRecurrence[{3, -3, 1}, {48, 194, 438}, 50] (* _Vincenzo Librandi_, Feb 05 2012

%o (MAGMA) I:=[48, 194, 438]; [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 05 2012

%o (PARI) for(n=1, 40, print1(49*n^2 - n", ")); \\ Vincenzo Librandi, Feb 05 2012

%Y Cf. A157924.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 09 2009

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Last modified December 4 21:33 EST 2016. Contains 278755 sequences.