A164136 a(n) = 11*n*(n+1).

0, 22, 66, 132, 220, 330, 462, 616, 792, 990, 1210, 1452, 1716, 2002, 2310, 2640, 2992, 3366, 3762, 4180, 4620, 5082, 5566, 6072, 6600, 7150, 7722, 8316, 8932, 9570, 10230, 10912, 11616, 12342, 13090, 13860, 14652, 15466, 16302, 17160, 18040, 18942, 19866, 20812

Offset: 0

Author

Vincenzo Librandi, Aug 11 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, A002378.

Programs

Magma

[11*n*(n+1): n in [0..40]]; // Vincenzo Librandi, Sep 12 2013

Mathematica

CoefficientList[Series[(22 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 12 2013 *)

PARI

a(n)=11*n*(n+1) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 22*A000217(n) = 11*A002378(n).

a(n) = 22*n + a(n-1) with n>0, a(0)=0. - Vincenzo Librandi, Nov 30 2010

G.f.: 22*x/(1-x)^3. - Vincenzo Librandi, Sep 12 2013

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Sep 12 2013

E.g.f.: 11*x*(2 + x)*exp(x). - G. C. Greubel, Sep 12 2017

From Amiram Eldar, Feb 22 2023: (Start)

Sum_{n>=1} 1/a(n) = 1/11.

Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/11.

Product_{n>=1} (1 - 1/a(n)) = -(11/Pi)*cos(sqrt(15/11)*Pi/2).

Product_{n>=1} (1 + 1/a(n)) = (11/Pi)*cos(sqrt(7/11)*Pi/2). (End)

Extensions

Offset corrected by R. J. Mathar, Aug 21 2009