A158396 729n^2 + 2n.

731, 2920, 6567, 11672, 18235, 26256, 35735, 46672, 59067, 72920, 88231, 105000, 123227, 142912, 164055, 186656, 210715, 236232, 263207, 291640, 321531, 352880, 385687, 419952, 455675, 492856, 531495, 571592, 613147, 656160, 700631, 746560

Offset

1,1

Comments

The identity (729*n+1)^2-(729*n^2+2*n)*(27)^2=1 can be written as A158397(n)^2-a(n)*(27)^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*(27^2*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*(731+727*x)/(1-x)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {731, 2920, 6567}, 50]

Prog

(Magma) I:=[731, 2920, 6567]; [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) = 729*n^2 + 2*n.

Crossrefs

Cf. A158397.

Sequence in context: A098292 A031525 A031705 * A098263 A289571 A098291

Adjacent sequences: A158393 A158394 A158395 * A158397 A158398 A158399

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved