A154519 a(n) = 216*n + 12.

228, 444, 660, 876, 1092, 1308, 1524, 1740, 1956, 2172, 2388, 2604, 2820, 3036, 3252, 3468, 3684, 3900, 4116, 4332, 4548, 4764, 4980, 5196, 5412, 5628, 5844, 6060, 6276, 6492, 6708, 6924, 7140, 7356, 7572, 7788, 8004, 8220, 8436, 8652

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 A154515(n)^2 - A154517(n)*a(n)^2 = 1 (see also the second comment at A154515).

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. A154515, A154517, A161705.

Programs

Magma

I:=[228, 444]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 30 2012

Mathematica

LinearRecurrence[{2, -1}, {228, 444}, 50] (* Vincenzo Librandi, Jan 30 2012 *)

PARI

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

Formula

G.f.: x*(228 - 12*x)/(x-1)^2. - Vincenzo Librandi, Jan 30 2012 [corrected by Georg Fischer, May 12 2019]

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 30 2012

a(n) = 12*A161705(n). - Michel Marcus, Aug 19 2018