A155212 a(n) = (n^2 + 9*n + 4)/2.

2, 7, 13, 20, 28, 37, 47, 58, 70, 83, 97, 112, 128, 145, 163, 182, 202, 223, 245, 268, 292, 317, 343, 370, 398, 427, 457, 488, 520, 553, 587, 622, 658, 695, 733, 772, 812, 853, 895, 938, 982, 1027, 1073, 1120, 1168, 1217, 1267, 1318, 1370, 1423, 1477, 1532

Offset: 0

Author

Vincenzo Librandi, Jan 22 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217.

Programs

Magma

I:=[2,7,13]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 26 2012

Mathematica

Table[(n^2 + 9 n + 4)/2, {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Jun 12 2011 *)
LinearRecurrence[{3, -3, 1}, {2, 7, 13}, 60] (* Harvey P. Dale, Aug 11 2014 *)

PARI

for(n=0, 60, print1((n^2+9*n+4)/2", ")); \\ Vincenzo Librandi, Feb 26 2012

Formula

G.f.: (-2 - x + 2*x^2)/(x - 1)^3. - R. J. Mathar, Mar 23 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 26 2012

Sum_{n>=0} 1/a(n) = 271/280 + 2*Pi*tan(sqrt(65)*Pi/2)/sqrt(65). - Amiram Eldar, Dec 13 2022

E.g.f.: exp(x)*(2 + 5*x + x^2/2). - Elmo R. Oliveira, Oct 21 2024

Extensions

Edited by Jon E. Schoenfield, Jun 23 2010

a(0)=2 from Vincenzo Librandi, Mar 22 2011