A158220 a(n) = 169*n^2 + 2*n.

171, 680, 1527, 2712, 4235, 6096, 8295, 10832, 13707, 16920, 20471, 24360, 28587, 33152, 38055, 43296, 48875, 54792, 61047, 67640, 74571, 81840, 89447, 97392, 105675, 114296, 123255, 132552, 142187, 152160, 162471, 173120, 184107, 195432

Offset

1,1

Comments

The identity (169*n + 1)^2 - (169*n^2 + 2*n)*(13)^2 = 1 can be written as A158221(n)^2 - a(n)*(13)^2 = 1. - Vincenzo Librandi, Feb 02 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 15 in the first table at p. 85, case d(t) = t*(13^2*t+2)).

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

Formula

G.f.: x*(-171 - 167*x)/(-1+x)^3. - Harvey P. Dale, Apr 19 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 02 2012

Mathematica

Table[169n^2+2n, {n, 40}] (* Harvey P. Dale, Apr 19 2011 *)
LinearRecurrence[{3, -3, 1}, {171, 680, 1527}, 50] (* Vincenzo Librandi, Feb 02 2012 *)

Prog

(Magma) I:=[171, 680, 1527]; [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 02 2012
(PARI) for(n=1, 22, print1(169*n^2 + 2*n", ")); \\ Vincenzo Librandi, Feb 02 2012

Crossrefs

Cf. A158221.

Sequence in context: A016057 A043407 A031691 * A079654 A220869 A251329

Adjacent sequences: A158217 A158218 A158219 * A158221 A158222 A158223

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 14 2009

Status

approved