A033578 a(n) = (3*n - 1)*(4*n - 1).

1, 6, 35, 88, 165, 266, 391, 540, 713, 910, 1131, 1376, 1645, 1938, 2255, 2596, 2961, 3350, 3763, 4200, 4661, 5146, 5655, 6188, 6745, 7326, 7931, 8560, 9213, 9890, 10591, 11316, 12065, 12838, 13635, 14456, 15301, 16170, 17063, 17980, 18921, 19886, 20875

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A033577.

Programs

GAP

List([0..50], n-> (3*n-1)*(4*n-1)); # G. C. Greubel, Oct 09 2019

Magma

[(3*n-1)*(4*n-1): n in [0..50]]; // G. C. Greubel, Oct 09 2019

Maple

seq((3*n-1)*(4*n-1),n=0..50); # Nathaniel Johnston, Jun 26 2011

Mathematica

Table[(3*n-1)*(4*n-1), {n, 0, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
LinearRecurrence[{3,-3,1},{1,6,35},50] (* Harvey P. Dale, Jul 19 2025 *)

PARI

a(n)=(3*n-1)*(4*n-1) \\ Charles R Greathouse IV, Jun 17 2017

Sage

[(3*n-1)*(4*n-1) for n in (0..50)] # G. C. Greubel, Oct 09 2019

Formula

From G. C. Greubel, Oct 09 2019: (Start)

G.f.: (1 + 3*x +20*x^2)/(1-x)^3.

E.g.f.: (1 + 5*x + 12*x^2)*exp(x). (End)