A158218 169n^2 - 2n.

167, 672, 1515, 2696, 4215, 6072, 8267, 10800, 13671, 16880, 20427, 24312, 28535, 33096, 37995, 43232, 48807, 54720, 60971, 67560, 74487, 81752, 89355, 97296, 105575, 114192, 123147, 132440, 142071, 152040, 162347, 172992, 183975, 195296

Offset

1,1

Comments

The identity (169*n-1)^2-(169*n^2-2*n)*(13)^2=1 can be written as A158219(n)^2-a(n)*(13)^2=1.

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

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).

G.f.: x*(-167-171*x)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {167, 672, 1515}, 50]

Prog

(Magma) I:=[167, 672, 1515]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 169*n^2 - 2*n.

Crossrefs

Cf. A158219.

Sequence in context: A142431 A142776 A362542 * A142287 A167574 A377180

Adjacent sequences: A158215 A158216 A158217 * A158219 A158220 A158221

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 14 2009

Status

approved