A158364 529n^2 - 2n.

527, 2112, 4755, 8456, 13215, 19032, 25907, 33840, 42831, 52880, 63987, 76152, 89375, 103656, 118995, 135392, 152847, 171360, 190931, 211560, 233247, 255992, 279795, 304656, 330575, 357552, 385587, 414680, 444831, 476040, 508307, 541632

Offset

1,1

Comments

The identity (529*n-1)^2-(529*n^2-2*n)*(23)^2=1 can be written as A158365(n)^2-a(n)*(23)^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*(23^2*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*(-527-531*x)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {527, 2112, 4755}, 50]

Prog

(Magma) I:=[527, 2112, 4755]; [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) = 529*n^2 - 2*n.

Crossrefs

Cf. A158365.

Sequence in context: A337779 A261075 A250754 * A232885 A085329 A157475

Adjacent sequences: A158361 A158362 A158363 * A158365 A158366 A158367

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 17 2009

Status

approved