A154267 a(n) = 27*n + 15.

15, 42, 69, 96, 123, 150, 177, 204, 231, 258, 285, 312, 339, 366, 393, 420, 447, 474, 501, 528, 555, 582, 609, 636, 663, 690, 717, 744, 771, 798, 825, 852, 879, 906, 933, 960, 987, 1014, 1041, 1068, 1095, 1122, 1149, 1176, 1203, 1230, 1257, 1284, 1311, 1338

Offset: 0

Author

Vincenzo Librandi, Jan 06 2009

Keywords

• nonn
• easy

Comments

The identity (81*n^2 + 90*n + 26)^2 - (9*n^2 + 10*n + 3)*(27*n + 15)^2 = 1 can be written as A154277(n+1)^2 - A154254(n+1)*a(n)^2 = 1. - Vincenzo Librandi, Feb 03 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A154254, A154277.

Programs

Magma

I:=[15, 42]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 02 2012

Mathematica

Range[15, 7000, 27] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
LinearRecurrence[{2, -1}, {15, 42}, 40] (* Vincenzo Librandi, Feb 02 2012 *)
27*Range[0,50]+15 (* Harvey P. Dale, Feb 26 2017 *)

PARI

a(n)=27*n+15 \\ Charles R Greathouse IV, Dec 28 2011

Formula

G.f.: 3*(5 + 4*x)/(1-x)^2. - R. J. Mathar, Jan 05 2011

a(n) = 3*A017221(n). - R. J. Mathar, Jan 05 2011

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 02 2012

E.g.f.: (27*x + 15)*exp(x). - G. C. Greubel, Sep 08 2016