A157447 a(n) = 512*n - 16.

496, 1008, 1520, 2032, 2544, 3056, 3568, 4080, 4592, 5104, 5616, 6128, 6640, 7152, 7664, 8176, 8688, 9200, 9712, 10224, 10736, 11248, 11760, 12272, 12784, 13296, 13808, 14320, 14832, 15344, 15856, 16368, 16880, 17392, 17904, 18416, 18928

Offset

1,1

Comments

The identity (2048*n^2 - 128*n + 1)^2 - (16*n^2 - n)*(512*n - 16)^2 = 1 can be written as A157448(n)^2 - A157446(n)*a(n)^2 = 1 (see also second comment at A157446). - Vincenzo Librandi, Jan 26 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 26 2012

G.f.: x*(16*x + 496)/(x-1)^2. - Vincenzo Librandi, Jan 26 2012

Mathematica

LinearRecurrence[{2, -1}, {496, 1008}, 40] (* Vincenzo Librandi, Jan 26 2012 *)
512*Range[50]-16 (* Harvey P. Dale, Apr 09 2019 *)

Prog

(Magma) I:=[496, 1008]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 26 2012
(PARI) for(n=1, 22, print1(512*n - 16", ")); \\ Vincenzo Librandi, Jan 26 2012

Crossrefs

Cf. A157446, A157448.

Sequence in context: A333756 A179170 A345351 * A109477 A302366 A303083

Adjacent sequences: A157444 A157445 A157446 * A157448 A157449 A157450

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 01 2009

Status

approved