A154266 a(n) = 27*n + 12.

12, 39, 66, 93, 120, 147, 174, 201, 228, 255, 282, 309, 336, 363, 390, 417, 444, 471, 498, 525, 552, 579, 606, 633, 660, 687, 714, 741, 768, 795, 822, 849, 876, 903, 930, 957, 984, 1011, 1038, 1065, 1092, 1119, 1146, 1173, 1200, 1227, 1254, 1281, 1308, 1335

Offset: 0

Author

Vincenzo Librandi, Jan 06 2009

Keywords

• nonn
• easy

Comments

The identity (81*n^2 + 72*n + 17)^2 - (9*n^2 + 8*n + 2)*(27*n + 12)^2 = 1 can be written as A154295(n+1)^2 - A154262(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. A008585, A017197, A017209, A154262, A154295.

Programs

Magma

I:=[12, 39]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Feb 02 2012

Mathematica

Range[12, 7000, 27] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
LinearRecurrence[{2, -1}, {12, 39}, 50] (* Vincenzo Librandi, Feb 02 2012 *)

PARI

a(n)=27*n+12 \\ Charles R Greathouse IV, Dec 28 2011

Formula

From R. J. Mathar, Jan 05 2011: (Start)

G.f.: 3*(4 + 5*x)/(1-x)^2.

a(n) = 3*A017209(n). (End)

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

E.g.f.: (27*x + 12)*exp(x). - G. C. Greubel, Sep 08 2016

a(n) = A017197(3*n+1) = A008585(9*n+4). - Elmo R. Oliveira, Apr 12 2025

Extensions

119 replaced by 1119 - R. J. Mathar, Jan 07 2009