%I #35 Aug 16 2024 23:13:08

%S 3,60,1008,16320,261888,4193280,67104768,1073725440,17179803648,

%T 274877644800,4398045462528,70368739983360,1125899890065408,

%U 18014398442373120,288230375883276288,4611686017353646080,73786976290543239168,1180591620700231434240,18889465931409861378048

%N Number of monic irreducible polynomials of degree 4 in GF(2^n)[x].

%H Vincenzo Librandi, <a href="/A115490/b115490.txt">Table of n, a(n) for n = 1..800</a>

%H Max Alekseyev, <a href="http://translate.google.com/translate?hl=en&amp;sl=ru&amp;tl=en&amp;u=http%3A%2F%2Fdxdy.ru%2Ftopic1165.html">Formula for the number of monic irreducible polynomials in a finite field</a>

%H Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI scripts for various problems</a>

%H Steven T. Dougherty and Esengül Saltürk, <a href="https://doi.org/10.3934/amc.2024035">The neighbor graph of binary self-orthogonal codes</a>, Adv. Math. Comm. (2024). See p. 16.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-64).

%F 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

%F G.f.: 3*x / ( (16*x-1)*(4*x-1) ). - _R. J. Mathar_, Jul 23 2014

%F a(n) = (16^n-4^n)/4. - _Vincenzo Librandi_, Jul 25 2014

%F E.g.f.: exp(4*x)*(exp(12*x) - 1)/4. - _Stefano Spezia_, Aug 16 2024

%t CoefficientList[Series[3/((16 x - 1) (4 x - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jul 25 2014 *)

%o (Magma) [(16^n-4^n)/4: n in [1..20]]; // _Vincenzo Librandi_, Jul 25 2014

%Y Cf. A115457-A115505.

%K nonn,easy

%O 1,1

%A _Max Alekseyev_, Jan 16 2006