A158230 256n^2+2n.

258, 1028, 2310, 4104, 6410, 9228, 12558, 16400, 20754, 25620, 30998, 36888, 43290, 50204, 57630, 65568, 74018, 82980, 92454, 102440, 112938, 123948, 135470, 147504, 160050, 173108, 186678, 200760, 215354, 230460, 246078, 262208, 278850, 296004

Offset

1,1

Comments

The identity (256*n+1)^2-(256*n^2+2*n)*(16)^2=1 can be written as A158231(n)^2-a(n)*(16)^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*(16^2*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*(-254*x-258)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {258, 1028, 2310}, 50]

Prog

(Magma) I:=[258, 1028, 2310]; [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) = 256*n^2+2*n.

Crossrefs

Cf. A158231.

Sequence in context: A339538 A252264 A202892 * A209945 A233306 A282060

Adjacent sequences: A158227 A158228 A158229 * A158231 A158232 A158233

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 14 2009

Status

approved