A179741 a(n) = (2*n+1)*(6*n-1).

-1, 15, 55, 119, 207, 319, 455, 615, 799, 1007, 1239, 1495, 1775, 2079, 2407, 2759, 3135, 3535, 3959, 4407, 4879, 5375, 5895, 6439, 7007, 7599, 8215, 8855, 9519, 10207, 10919, 11655, 12415, 13199, 14007, 14839, 15695, 16575, 17479, 18407

Offset: 0

Author

Paul Curtz, Jan 10 2011

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A061037, A077591, A184005.

Programs

Magma

[(2*n+1)*(6*n-1): n in [0..50]]; // Vincenzo Librandi, Aug 04 2011

Mathematica

Table[12n^2+4n-1,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{-1,15,55},40] (* Harvey P. Dale, Dec 17 2013 *)

PARI

a(n)=(2*n+1)*(6*n-1) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = a(n-1) + 24*n + 16.

a(n) = 2*a(n-1) - a(n-2) + 16.

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

a(n) = A077591(n+1) + A061037(2*n-1).

From Bruno Berselli, Jan 25 2011: (Start)

G.f.: (-1 +18*x +7*x^2)/(1-x)^3.

a(n) = A184005(4*n) (n>0). (End)

E.g.f.: (-1 + 16*x + 12*x^2)*exp(x). - G. C. Greubel, Jul 22 2017

From Amiram Eldar, Oct 08 2023: (Start)

Sum_{n>=1} 1/a(n) = (3*log(3) - Pi*sqrt(3) + 4)/16.

Sum_{n>=1} (-1)^(n+1)/a(n) = (3*Pi - 2*sqrt(3)*log(sqrt(3)+2) - 4)/16. (End)

Extensions

Edited by N. J. A. Sloane, Jan 12 2011