A158252 289n^2 - 2n.

287, 1152, 2595, 4616, 7215, 10392, 14147, 18480, 23391, 28880, 34947, 41592, 48815, 56616, 64995, 73952, 83487, 93600, 104291, 115560, 127407, 139832, 152835, 166416, 180575, 195312, 210627, 226520, 242991, 260040, 277667, 295872, 314655

Offset

1,1

Comments

The identity (289*n-1)^2-(289*n^2-2*n)*(17)^2=1 can be written as A158253(n)^2-a(n)*(17)^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*(17^2*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*(-287-291*x)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {287, 1152, 2595}, 50]

Prog

(Magma) I:=[287, 1152, 2595]; [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) = 289*n^2 - 2*n.

Crossrefs

Cf. A158253.

Sequence in context: A157997 A063362 A159949 * A236869 A158287 A112245

Adjacent sequences: A158249 A158250 A158251 * A158253 A158254 A158255

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 15 2009

Status

approved