A115489 Number of monic irreducible polynomials of degree 3 in GF(2^n)[x].

2, 20, 168, 1360, 10912, 87360, 699008, 5592320, 44739072, 357913600, 2863310848, 22906490880, 183251935232, 1466015498240, 11728124018688, 93824992215040, 750599937851392, 6004799503073280, 48038396025110528

Offset: 1

Author

Max Alekseyev, Jan 16 2006

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Max Alekseyev, Formula for the number of monic irreducible polynomials in a finite field
• Max Alekseyev, PARI scripts for various problems
• Index entries for linear recurrences with constant coefficients, signature (10,-16).

Crossrefs

Cf. A115457-A115505.

Programs

Magma

[-(1/3)*2^n+(1/3)*8^n: n in [1..20]]; // Vincenzo Librandi, Jul 25 2014

Mathematica

LinearRecurrence[{10,-16},{2,20},30] (* Harvey P. Dale, Sep 25 2013 *)
CoefficientList[Series[2/((8 x - 1) (2 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 25 2014 *)

Formula

a(0)=0, a(1)=2, a(n)=10a(n-1)-16a(n-2). - T. D. Noe, Nov 30 2006

G.f.: 2*x / ( (8*x-1)*(2*x-1) ). - R. J. Mathar, Jul 23 2014