A158392 676n^2 - 2n.

674, 2700, 6078, 10808, 16890, 24324, 33110, 43248, 54738, 67580, 81774, 97320, 114218, 132468, 152070, 173024, 195330, 218988, 243998, 270360, 298074, 327140, 357558, 389328, 422450, 456924, 492750, 529928, 568458, 608340, 649574, 692160

Offset

1,1

Comments

The identity (676*n-1)^2-(676*n^2-2*n)*(26)^2=1 can be written as A158393(n)^2-a(n)*(26)^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*(26^2*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*(-674-678*x)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {674, 2700, 6078}, 50]

Prog

(Magma) I:=[674, 2700, 6078]; [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) = 676*n^2 - 2*n.

Crossrefs

Cf. A158393.

Sequence in context: A234117 A171266 A267818 * A264328 A124942 A158393

Adjacent sequences: A158389 A158390 A158391 * A158393 A158394 A158395

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved