A157475 a(n) = 512n + 16.

528, 1040, 1552, 2064, 2576, 3088, 3600, 4112, 4624, 5136, 5648, 6160, 6672, 7184, 7696, 8208, 8720, 9232, 9744, 10256, 10768, 11280, 11792, 12304, 12816, 13328, 13840, 14352, 14864, 15376, 15888, 16400, 16912, 17424, 17936, 18448, 18960

Offset: 1

Author

Vincenzo Librandi, Mar 01 2009

Keywords

• nonn
• easy

Comments

The identity (2048*n^2+128*n+1)^2-(16*n^2+n)*(512*n+16)^2=1 can be written as A157476(n)^2-A157474(n)*a(n)^2=1 (see also second comment in A157476). [rewritten by Bruno Berselli, Aug 22 2011]

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).

Crossrefs

Cf. A157474, A157476.

Programs

Mathematica

512*Range[40]+16 (* or *) LinearRecurrence[{2,-1},{528,1040},40] (* Harvey P. Dale, Dec 07 2011 *)

Formula

G.f.: 16*x*(33-x)/(1-x)^2. - Bruno Berselli, Aug 22 2011

a(1)=528, a(2)=1040, a(n) = 2*a(n-1)-a(n-2). - Harvey P. Dale, Dec 07 2011