A033566 a(n) = (2*n+1) * (4*n-1).

-1, 9, 35, 77, 135, 209, 299, 405, 527, 665, 819, 989, 1175, 1377, 1595, 1829, 2079, 2345, 2627, 2925, 3239, 3569, 3915, 4277, 4655, 5049, 5459, 5885, 6327, 6785, 7259, 7749, 8255, 8777, 9315, 9869, 10439, 11025, 11627, 12245, 12879, 13529, 14195, 14877, 15575, 16289, 17019, 17765

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A004767, A005408.

Programs

GAP

List([0..50], n-> (2*n+1)*(4*n-1)); # G. C. Greubel, Oct 12 2019

Magma

[(2*n+1)*(4*n-1): n in [0..50]]; // G. C. Greubel, Oct 12 2019

Maple

seq((2*n+1)*(4*n-1), n=0..50); # G. C. Greubel, Oct 12 2019

Mathematica

Table[(2*n+1)*(4*n-1), {n, 0, 50}] (* G. C. Greubel, Oct 12 2019 *)

PARI

a(n) = (2*n+1) * (4*n-1); \\ Michel Marcus, Oct 03 2016

Sage

[(2*n+1)*(4*n-1) for n in range(50)] # G. C. Greubel, Oct 12 2019

Formula

a(n) = A005408(n) * A004767(n-1). - Michel Marcus, Oct 03 2016

From G. C. Greubel, Oct 12 2019: (Start)

G.f.: (-1 + 12*x + 5*x^2)/(1-x)^3.

E.g.f.: (-1 + 10*x + 8*x^2)*exp(x). (End)

Sum_{n>=0} 1/a(n) = -2/3 +log(2)/6-Pi/12 = -0.81294152437.. - R. J. Mathar, May 07 2024

Extensions

Terms a(37) onward added by G. C. Greubel, Oct 12 2019