A115490 Number of monic irreducible polynomials of degree 4 in GF(2^n)[x].
3, 60, 1008, 16320, 261888, 4193280, 67104768, 1073725440, 17179803648, 274877644800, 4398045462528, 70368739983360, 1125899890065408, 18014398442373120, 288230375883276288, 4611686017353646080, 73786976290543239168, 1180591620700231434240, 18889465931409861378048
Offset: 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
- Steven T. Dougherty and Esengül Saltürk, The neighbor graph of binary self-orthogonal codes, Adv. Math. Comm. (2024). See p. 16.
- Index entries for linear recurrences with constant coefficients, signature (20,-64).
Programs
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Magma
[(16^n-4^n)/4: n in [1..20]]; // Vincenzo Librandi, Jul 25 2014
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Mathematica
CoefficientList[Series[3/((16 x - 1) (4 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 25 2014 *)
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