A111144 a(n) = n*(n+13)*(n+14)/6.

0, 35, 80, 136, 204, 285, 380, 490, 616, 759, 920, 1100, 1300, 1521, 1764, 2030, 2320, 2635, 2976, 3344, 3740, 4165, 4620, 5106, 5624, 6175, 6760, 7380, 8036, 8729, 9460, 10230, 11040, 11891, 12784, 13720, 14700, 15725, 16796, 17914, 19080, 20295, 21560

Offset: 0

Author

Jonathan Vos Post, Nov 12 2005

Keywords

• easy
• nonn

Comments

After a(1) all values have at least three prime factors with multiplicity, for example a(33) = 11891 = 11 * 23 * 47 and a(49) = 31899 = 3 * 7^3 * 31.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000292, A111396.

Programs

Magma

[n*(n+13)*(n+14)/6: n in [0..50]]; // Vincenzo Librandi, Jan 11 2012

Mathematica

Table[n (n + 13) (n + 14)/6, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)

PARI

a(n)=n*(n+13)*(n+14)/6 \\ Charles R Greathouse IV, Jan 11 2012

Formula

a(n) = A000292(n) + 4n^2 + 30n.

G.f.: x*(35 - 60*x + 26*x^2)/(1-x)^4. - Colin Barker, Jan 11 2012

From Amiram Eldar, Jul 30 2024: (Start)

Sum_{n>=1} 1/a(n) = 811373/65585520.

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/13 - 752153/7287280. (End)