A115491 Number of monic irreducible polynomials of degree 5 in GF(2^n)[x].

6, 204, 6552, 209712, 6710880, 214748352, 6871947648, 219902325504, 7036874417664, 225179981368320, 7205759403792384, 230584300921368576, 7378697629483819008, 236118324143482257408, 7555786372591432335360

Offset: 1

Author

Max Alekseyev, Jan 16 2006

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..670
• 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 (34,-64).

Crossrefs

Cf. A115457-A115505.

Programs

Magma

[(32^(n+1)-16*2^(n+1))/160: n in [1..20]]; // Vincenzo Librandi, Jul 25 2014

Mathematica

CoefficientList[Series[6/((32 x - 1) (2 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 25 2014 *)

Formula

a(0)=0, a(1)=6; for n>1, a(n)=34*a(n-1)-64*a(n-2). - T. D. Noe, Nov 30 2006

G.f.: 6*x / ( (32*x-1)*(2*x-1) ). - R. J. Mathar, Jul 23 2014