A173267 - OEIS

A173267

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

122, 486, 1092, 1940, 3030, 4362, 5936, 7752, 9810, 12110, 14652, 17436, 20462, 23730, 27240, 30992, 34986, 39222, 43700, 48420, 53382, 58586, 64032, 69720, 75650, 81822, 88236, 94892, 101790, 108930, 116312, 123936, 131802, 139910, 148260, 156852, 165686, 174762, 184080, 193640, 203442, 213486, 223772

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OFFSET

1,1

COMMENTS

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 14 in the first table at p. 85, case d(t) = t*(11^2*t+1)).

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: x*(-122 - 120*x)/(x-1)^3. - Vincenzo Librandi, Feb 06 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 06 2012

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {122, 486, 1092}, 50] (* Vincenzo Librandi, Feb 06 2012 *)

Table[121n^2+n, {n, 50}] (* Harvey P. Dale, Dec 15 2019 *)

PROG

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

(PARI) for(n=1, 50, print1(121*n^2 + n", ")); \\ Vincenzo Librandi, Feb 06 2012

CROSSREFS

Cf. A157958.