A033587 a(n) = 2*n*(4*n + 3).

0, 14, 44, 90, 152, 230, 324, 434, 560, 702, 860, 1034, 1224, 1430, 1652, 1890, 2144, 2414, 2700, 3002, 3320, 3654, 4004, 4370, 4752, 5150, 5564, 5994, 6440, 6902, 7380, 7874, 8384, 8910, 9452, 10010, 10584, 11174, 11780, 12402, 13040, 13694, 14364, 15050

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

The inverse binomial transform is [0, 14, 16, 0, 0, 0, ...]. - R. J. Mathar, May 06 2008

Sequence found by reading the line from 0, in the direction 0, 14, ..., in the square spiral whose vertices are the triangular numbers A000217. Opposite numbers to the even hexagonal numbers A014635 in the same spiral. - Omar E. Pol, Sep 03 2011

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Programs

Mathematica

Table[2*n(4*n + 3), {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
LinearRecurrence[{3,-3,1},{0,14,44},80] (* Harvey P. Dale, Jun 05 2019 *)

PARI

a(n)=2*n*(4*n+3) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 2*A033954(n).

O.g.f.: 2*x*(7+x)/(1-x)^3. - R. J. Mathar, May 06 2008

a(n) = 16*n + a(n-1) - 2 with a(0)=0. - Vincenzo Librandi, Aug 05 2010

E.g.f.: (8*x^2 + 14*x)*exp(x). - G. C. Greubel, Jul 18 2017

From Vaclav Kotesovec, Aug 18 2018: (Start)

Sum_{n>=1} 1/a(n) = 2/9 + Pi/12 - log(2)/2.

Sum_{n>=1} (-1)^n/a(n) = 2/9 - Pi/(6*sqrt(2)) - log(2)/6 + log(1+sqrt(2))/(3*sqrt(2)). (End)