A154518 a(n) = 216*n - 12.

204, 420, 636, 852, 1068, 1284, 1500, 1716, 1932, 2148, 2364, 2580, 2796, 3012, 3228, 3444, 3660, 3876, 4092, 4308, 4524, 4740, 4956, 5172, 5388, 5604, 5820, 6036, 6252, 6468, 6684, 6900, 7116, 7332, 7548, 7764, 7980, 8196, 8412, 8628

Offset: 1

Author

Vincenzo Librandi, Jan 11 2009

Keywords

• nonn
• easy

Comments

The identity (648*n^2 - 72*n + 1)^2 - (9*n^2 - n)*(216*n - 12)^2 = 1 can be written as A154514(n)^2 - A154516(n)*a(n)^2 = 1 (see also the second comment at A154514). - Vincenzo Librandi, Jan 30 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A154514, A154516.

Programs

Magma

I:=[204, 420]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 30 2012

Mathematica

216Range[40]-12  (* Harvey P. Dale, Feb 01 2011 *)
LinearRecurrence[{2, -1}, {204, 420}, 50] (* Vincenzo Librandi, Jan 30 2012 *)

PARI

a(n)=216*n-12 \\ Charles R Greathouse IV, Dec 27 2011

Formula

From R. J. Mathar, Jul 29 2009: (Start)

a(n) = 12*(18n-1).

O.g.f.: 12*x*(17+x)/(x-1)^2. (End)

a(n) = 2*a(n-1) - a(n-2).