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

0,2

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).

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)

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 *)

Prog

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

Crossrefs

Sequence in context: A064125 A089031 A265152 * A189807 A009942 A031130

Adjacent sequences: A033584 A033585 A033586 * A033588 A033589 A033590

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved