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A173267 a(n) = 121*n^2 + n. 2

%I #26 Sep 08 2022 08:45:50

%S 122,486,1092,1940,3030,4362,5936,7752,9810,12110,14652,17436,20462,

%T 23730,27240,30992,34986,39222,43700,48420,53382,58586,64032,69720,

%U 75650,81822,88236,94892,101790,108930,116312,123936,131802,139910,148260,156852,165686,174762,184080,193640,203442,213486,223772

%N a(n) = 121*n^2 + n.

%C The identity (242*n + 1)^2 - (121*n^2 + n)*22^2 = 1 can be written as A157958(n)^2 - a(n)*22^2 = 1. - _Vincenzo Librandi_, Feb 06 2012

%H Vincenzo Librandi, <a href="/A173267/b173267.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 14 in the first table at p. 85, case d(t) = t*(11^2*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*(-122 - 120*x)/(x-1)^3. - _Vincenzo Librandi_, Feb 06 2012

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Feb 06 2012

%t LinearRecurrence[{3, -3, 1}, {122, 486, 1092}, 50] (* _Vincenzo Librandi_, Feb 06 2012 *)

%t Table[121n^2+n,{n,50}] (* _Harvey P. Dale_, Dec 15 2019 *)

%o (Magma)[121*n^2+n: n in [1..50]];

%o (PARI) for(n=1, 50, print1(121*n^2 + n", ")); \\ _Vincenzo Librandi_, Feb 06 2012

%Y Cf. A157958.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Nov 22 2010

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)