A173307 a(n) = 13*n*(n+1).

0, 26, 78, 156, 260, 390, 546, 728, 936, 1170, 1430, 1716, 2028, 2366, 2730, 3120, 3536, 3978, 4446, 4940, 5460, 6006, 6578, 7176, 7800, 8450, 9126, 9828, 10556, 11310, 12090, 12896, 13728, 14586, 15470, 16380, 17316, 18278, 19266, 20280, 21320, 22386, 23478, 24596

Offset: 0

Author

Vincenzo Librandi, Feb 16 2010

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, A152741, A262221.

Programs

Magma

[13*n*(n+1): n in [0..40]]; // Vincenzo Librandi, Sep 28 2013

Magma

I:=[0, 26, 78]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Sep 28 2013

Mathematica

Table[13 n (n + 1), {n, 0, 50}] (* or *) CoefficientList[Series[26 x/(1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Sep 28 2013 *)
LinearRecurrence[{3,-3,1},{0,26,78},50] (* Harvey P. Dale, Apr 08 2014 *)

PARI

a(n)=13*n*(n+1) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 26*A000217(n).

From Vincenzo Librandi, Sep 28 2013: (Start)

G.f.: 26*x/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

From Amiram Eldar, Feb 22 2023: (Start)

Sum_{n>=1} 1/a(n) = 1/13.

Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/13.

Product_{n>=1} (1 - 1/a(n)) = -(13/Pi)*cos(sqrt(17/13)*Pi/2).

Product_{n>=1} (1 + 1/a(n)) = (13/Pi)*cos(3*Pi/(2*sqrt(13))). (End)

From Elmo R. Oliveira, Dec 14 2024: (Start)

E.g.f.: 13*exp(x)*x*(2 + x).

a(n) = 13*A002378(n) = 2*A152741(n). (End)

Extensions

Incorrect formulas and examples deleted by R. J. Mathar, Jan 04 2011