A115504 Number of monic irreducible polynomials of degree 1 in GF(2^n)[x1,x2,x3,x4,x5].

62, 1364, 37448, 1118480, 34636832, 1090785344, 34630287488, 1103823438080, 35253226045952, 1127000493261824, 36046397799139328, 1153203048319815680, 36897992296869404672, 1180663682709764194304

Offset: 1

Author

Max Alekseyev, Jan 16 2006

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..670
• Max Alekseyev, Formula for the number of monic irreducible polynomials in a finite field
• Max Alekseyev, PARI scripts for various problems
• Index entries for linear recurrences with constant coefficients, signature (62,-1240,9920,-31744,32768).

Crossrefs

Cf. A115457-A115505.

Programs

Magma

[2^n+4^n+8^n+16^n+32^n: n in [1..20]]; // Vincenzo Librandi, Jul 25 2014

Mathematica

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 *)
LinearRecurrence[{62,-1240,9920,-31744,32768},{62,1364,37448,1118480,34636832},20] (* Harvey P. Dale, Oct 07 2019 *)

Formula

a(n) = A034665(n) - 1, or a(n) = 2^n + 4^n + 8^n + 16^n + 32^n. - Chris Boyd, Apr 26 2014

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