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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, 73786976290543239168, 1180591620700231434240, 18889465931409861378048
OFFSET
1,1
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
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
E.g.f.: exp(4*x)*(exp(12*x) - 1)/4. - Stefano Spezia, Aug 16 2024
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
KEYWORD
nonn,easy
AUTHOR
Max Alekseyev, Jan 16 2006
STATUS
approved