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A115490 Number of monic irreducible polynomials of degree 4 in GF(2^n)[x]. 4
3, 60, 1008, 16320, 261888, 4193280, 67104768, 1073725440, 17179803648, 274877644800, 4398045462528, 70368739983360, 1125899890065408, 18014398442373120, 288230375883276288, 4611686017353646080 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..800

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 (20,-64).

FORMULA

a(0)=0, a(1)=3; for n>1, a(n) = 20*a(n-1)-64*a(n-2). - T. D. Noe, Nov 30 2006

a(n+1) = 4*16^n-4^n, with n>=0. - Paolo P. Lava, Jun 16 2008

G.f.: 3*x / ( (16*x-1)*(4*x-1) ). - R. J. Mathar, Jul 23 2014

a(n) = (16^n-4^n)/4. - Vincenzo Librandi, Jul 25 2014

MATHEMATICA

CoefficientList[Series[3/((16 x - 1) (4 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 25 2014 *)

PROG

(MAGMA) [(16^n-4^n)/4: n in [1..20]]; // Vincenzo Librandi, Jul 25 2014

CROSSREFS

Cf. A115457-A115505.

Sequence in context: A006432 A195550 A144659 * A065889 A183251 A001084

Adjacent sequences:  A115487 A115488 A115489 * A115491 A115492 A115493

KEYWORD

nonn,easy

AUTHOR

Max Alekseyev, Jan 16 2006

STATUS

approved

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Last modified July 8 22:01 EDT 2020. Contains 335537 sequences. (Running on oeis4.)