A158413 961n^2 + 2n.

963, 3848, 8655, 15384, 24035, 34608, 47103, 61520, 77859, 96120, 116303, 138408, 162435, 188384, 216255, 246048, 277763, 311400, 346959, 384440, 423843, 465168, 508415, 553584, 600675, 649688, 700623, 753480, 808259, 864960, 923583, 984128

Offset

1,1

Comments

The identity (961*n+1)^2-(961*n^2+2*n)*(31)^2=1 can be written as A158414(n)^2-a(n)*(31)^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*(31^2*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*(963+959*x)/(1-x)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {963, 3848, 8655}, 50]

Prog

(Magma) I:=[963, 3848, 8655]; [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) = 961*n^2 + 2n.

Crossrefs

Cf. A158414.

Sequence in context: A031529 A347884 A031709 * A252413 A267973 A267996

Adjacent sequences: A158410 A158411 A158412 * A158414 A158415 A158416

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved