A033576 a(n) = (2*n+1)*(12*n+1).

1, 39, 125, 259, 441, 671, 949, 1275, 1649, 2071, 2541, 3059, 3625, 4239, 4901, 5611, 6369, 7175, 8029, 8931, 9881, 10879, 11925, 13019, 14161, 15351, 16589, 17875, 19209, 20591, 22021, 23499, 25025

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A005408, A017533.

Programs

GAP

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

Magma

[(2*n+1)*(12*n+1): n in [0..50]]; // Vincenzo Librandi, Jul 07 2012

Maple

A033576:=n->(2*n+1)*(12*n+1); seq(A033576(n), n=0..50); # Wesley Ivan Hurt, Feb 02 2014

Mathematica

Table[(2n+1)(12n+1),{n,0,50}]  (* Harvey P. Dale, Mar 30 2011 *)
CoefficientList[Series[(1+36*x+11*x^2)/(1-x)^3,{x,0,50}],x] (* Vincenzo Librandi, Jul 07 2012 *)

PARI

a(n)=(2*n+1)*(12*n+1) \\ Charles R Greathouse IV, Jun 17 2017

Sage

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

Formula

From Colin Barker, Jun 10 2012: (Start)

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

G.f.: (1 + 36*x + 11*x^2)/(1-x)^3. (End)

a(n) = A005408(n) * A017533(n). - Wesley Ivan Hurt, Feb 02 2014

E.g.f.: (1 + 38*x + 24*x^2)*exp(x). - G. C. Greubel, Oct 12 2019