A158367 529n^2 + 2n.

531, 2120, 4767, 8472, 13235, 19056, 25935, 33872, 42867, 52920, 64031, 76200, 89427, 103712, 119055, 135456, 152915, 171432, 191007, 211640, 233331, 256080, 279887, 304752, 330675, 357656, 385695, 414792, 444947, 476160, 508431, 541760

Offset

1,1

Comments

The identity (529*n+1)^2-(529*n^2+2*n)*(23)^2=1 can be written as A158368(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*(531+527*x)/(1-x)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {531, 2120, 4767}, 50]

Prog

(Magma) I:=[531, 2120, 4767]; [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. A158368.

Sequence in context: A031521 A156772 A031701 * A225937 A225936 A098257

Adjacent sequences: A158364 A158365 A158366 * A158368 A158369 A158370

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 17 2009

Status

approved