A115491 - OEIS

%I #45 Feb 24 2024 01:14:15

%S 6,204,6552,209712,6710880,214748352,6871947648,219902325504,

%T 7036874417664,225179981368320,7205759403792384,230584300921368576,

%U 7378697629483819008,236118324143482257408,7555786372591432335360

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

%H Vincenzo Librandi, <a href="/A115491/b115491.txt">Table of n, a(n) for n = 1..670</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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (34,-64).

%F 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

%F G.f.: 6*x / ( (32*x-1)*(2*x-1) ). - _R. J. Mathar_, Jul 23 2014

%t CoefficientList[Series[6/((32 x - 1) (2 x - 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 25 2014 *)

%o (Magma) [(32^(n+1)-16*2^(n+1))/160: 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