A158131 - OEIS

%I #23 Oct 17 2022 17:32:20

%S 122,243,364,485,606,727,848,969,1090,1211,1332,1453,1574,1695,1816,

%T 1937,2058,2179,2300,2421,2542,2663,2784,2905,3026,3147,3268,3389,

%U 3510,3631,3752,3873,3994,4115,4236,4357,4478,4599,4720,4841,4962,5083,5204

%N a(n) = 121*n + 1.

%C The identity (121*n+1)^2-(121*n^2+2*n)*(11)^2=1 can be written as a(n)^2-A181679(n)*(11)^2=1.

%H Vincenzo Librandi, <a href="/A158131/b158131.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> [broken link]

%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*(11^2*t+2)).

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

%F a(n) = 2*a(n-1)-a(n-2).

%F G.f.: x*(122-x)/(1-x)^2.

%t LinearRecurrence[{2,-1},{122,243},50]

%t 121*Range[50]+1 (* _Harvey P. Dale_, Oct 17 2022 *)

%o (Magma) I:=[122, 243]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

%o (PARI) a(n) = 121*n + 1.

%Y Cf. A181679.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 13 2009