A158309 361n^2 + 2n.

363, 1448, 3255, 5784, 9035, 13008, 17703, 23120, 29259, 36120, 43703, 52008, 61035, 70784, 81255, 92448, 104363, 117000, 130359, 144440, 159243, 174768, 191015, 207984, 225675, 244088, 263223, 283080, 303659, 324960, 346983, 369728

Offset

1,1

Comments

The identity (361*n+1)^2-(361*n^2+2*n)*(19)^2=1 can be written as A158310(n)^2-a(n)*(19)^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*(19^2*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*(363+359*x)/(1-x)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {363, 1448, 3255}, 50]

Prog

(Magma) I:=[363, 1448, 3255]; [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) = 361*n^2 + 2*n.

Crossrefs

Cf. A158310.

Sequence in context: A192449 A116285 A031697 * A098251 A115464 A004534

Adjacent sequences: A158306 A158307 A158308 * A158310 A158311 A158312

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2009

Status

approved