A173308 a(n) = 17*n*(n+1).

0, 34, 102, 204, 340, 510, 714, 952, 1224, 1530, 1870, 2244, 2652, 3094, 3570, 4080, 4624, 5202, 5814, 6460, 7140, 7854, 8602, 9384, 10200, 11050, 11934, 12852, 13804, 14790, 15810, 16864, 17952, 19074, 20230, 21420, 22644, 23902, 25194, 26520, 27880, 29274, 30702

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, A195037.

Programs

Magma

[17*n*(n+1): n in [0..50]]; // Vincenzo Librandi, Aug 20 2014

Mathematica

Table[17n(n+1),{n,0,40}]  (* Harvey P. Dale, Apr 06 2011 *)

PARI

a(n)=34*binomial(n+1,2) \\ Charles R Greathouse IV, Jan 25 2012

Formula

a(n) = 34*A000217(n).

From Colin Barker, Jan 25 2012: (Start)

a(0)=0, a(1)=34, a(2)=102, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: 34*x/(1-x)^3. (End)

From Amiram Eldar, Feb 22 2023: (Start)

Sum_{n>=1} 1/a(n) = 1/17.

Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/17.

Product_{n>=1} (1 - 1/a(n)) = -(17/Pi)*cos(sqrt(21/17)*Pi/2).

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

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

E.g.f.: 17*exp(x)*x*(2 + x).

a(n) = 17*A002378(n) = 2*A195037(n). (End)

Extensions

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