%I #28 Sep 08 2022 08:45:23
%S 62,1364,37448,1118480,34636832,1090785344,34630287488,1103823438080,
%T 35253226045952,1127000493261824,36046397799139328,
%U 1153203048319815680,36897992296869404672,1180663682709764194304
%N Number of monic irreducible polynomials of degree 1 in GF(2^n)[x1,x2,x3,x4,x5].
%H Vincenzo Librandi, <a href="/A115504/b115504.txt">Table of n, a(n) for n = 1..670</a>
%H Max Alekseyev, <a href="http://translate.google.com/translate?hl=en&sl=ru&tl=en&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_05">Index entries for linear recurrences with constant coefficients</a>, signature (62,-1240,9920,-31744,32768).
%F a(n) = A034665(n) - 1, or a(n) = 2^n + 4^n + 8^n + 16^n + 32^n. - _Chris Boyd_, Apr 26 2014
%F G.f.: -2*x*( 31-1240*x+14880*x^2-63488*x^3+81920*x^4 ) / ( (4*x-1)*(2*x-1)*(8*x-1)*(16*x-1)*(32*x-1) ). - _R. J. Mathar_, Jul 23 2014
%t CoefficientList[Series[-2 (31 - 1240 x + 14880 x^2 - 63488 x^3 + 81920 x^4)/((4 x - 1) (2 x - 1) (8 x - 1) (16 x - 1) (32 x - 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 25 2014 *)
%t LinearRecurrence[{62,-1240,9920,-31744,32768},{62,1364,37448,1118480,34636832},20] (* _Harvey P. Dale_, Oct 07 2019 *)
%o (Magma) [2^n+4^n+8^n+16^n+32^n: 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