A158329 a(n) = 484*n^2 - 2*n.

482, 1932, 4350, 7736, 12090, 17412, 23702, 30960, 39186, 48380, 58542, 69672, 81770, 94836, 108870, 123872, 139842, 156780, 174686, 193560, 213402, 234212, 255990, 278736, 302450, 327132, 352782, 379400, 406986, 435540, 465062, 495552

Offset

1,1

Comments

The identity (484*n-1)^2-(484*n^2-2*n)*(22)^2=1 can be written as A158330(n)^2-a(n)*(22)^2=1.

Links

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

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*(22^2*t-2)).

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

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*(-482-486*x)/(x-1)^3.

E.g.f.: 2*exp(x)*x*(241 + 242*x). - Stefano Spezia, Aug 31 2024

Mathematica

LinearRecurrence[{3, -3, 1}, {482, 1932, 4350}, 50]

Prog

(Magma) I:=[482, 1932, 4350]; [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) = 484*n^2 - 2*n

Crossrefs

Cf. A158330.

Sequence in context: A214170 A304325 A175536 * A231395 A263291 A121734

Adjacent sequences: A158326 A158327 A158328 * A158330 A158331 A158332

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2009

Status

approved