A115492 Number of monic irreducible polynomials of degree 2 in GF(2^n)[x,y].

35, 1134, 34748, 1081080, 34077680, 1082126304, 34493939648, 1101659045760, 35218731564800, 1126449661607424, 36037593107790848, 1153062242078423040, 36895739947165675520, 1180627649514161823744, 37779508323708391374848, 1208935042986661734481920

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 (54,-808,3456,-4096).

Crossrefs

Cf. A115457-A115505.

Programs

Mathematica

CoefficientList[Series[7 (256 x^2 - 108 x + 5)/((2 x - 1) (4 x - 1) (16 x - 1) (32 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 26 2014 *)

PARI

Vec(7*x*(256*x^2-108*x+5)/((2*x-1)*(4*x-1)*(16*x-1)*(32*x-1)) + O(x^100)) \\ Colin Barker, Jul 25 2014

Formula

a(n) = 54*a(n-1)-808*a(n-2)+3456*a(n-3)-4096*a(n-4). - Colin Barker, Jul 25 2014

G.f.: 7*x*(256*x^2-108*x+5) / ((2*x-1)*(4*x-1)*(16*x-1)*(32*x-1)). - Colin Barker, Jul 25 2014

Extensions

More terms from Colin Barker, Jul 25 2014