cp's OEIS Frontend

A038518 Number of elements of GF(2^n) with trace 0 and subtrace 0.

%I A038518 #26 Mar 31 2020 19:37:03
%S A038518 0,1,1,1,6,6,16,36,56,136,256,496,1056,2016,4096,8256,16256,32896,
%T A038518 65536,130816,262656,523776,1048576,2098176,4192256,8390656,16777216,
%U A038518 33550336,67117056,134209536,268435456,536887296,1073709056,2147516416
%N A038518 Number of elements of GF(2^n) with trace 0 and subtrace 0.
%H A038518 Colin Barker, <a href="/A038518/b038518.txt">Table of n, a(n) for n = 0..1000</a>
%H A038518 F. Ruskey, <a href="http://combos.org/TSpoly">Number of irreducible polynomials over GF(2) with given trace and subtrace</a>
%H A038518 F. Ruskey, <a href="http://combos.org/TSGF2">Number of elements of GF(2^n) with given trace and subtrace</a>
%H A038518 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,4).
%F A038518 C(n, r+0)+C(n, r+4)+C(n, r+8)+... where r = 0 if n odd, r = 2 if n even.
%F A038518 G.f.: (-x^3+x^2+x)/[(1-2x)(1+2x+2x^2)].
%F A038518 a(0)=0; a(n) = ( 2^n - (-1-i)^n - (-1+i)^n )/4, i=sqrt(-1). - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 16 2004
%F A038518 a(n) = 2*a(n-2) + 4*a(n-3) for n>3. - _Colin Barker_, Aug 02 2019
%p A038518 0,seq(1/4*2^k-1/4*(-1-I)^k-1/4*(-1+I)^k,k=1..40); seq(coeff(convert(series((-x^3+x^2+x)/((1-2*x)*(1+2*x+2*x^2)),x,50),polynom),x,i),i=0..40); # C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 16 2004
%t A038518 LinearRecurrence[{0,2,4},{0,1,1,1},40] (* _Harvey P. Dale_, Mar 31 2020 *)
%o A038518 (PARI) concat(0, Vec(x*(1 + x - x^2) / ((1 - 2*x)*(1 + 2*x + 2*x^2)) + O(x^40))) \\ _Colin Barker_, Aug 02 2019
%Y A038518 Cf. A038503, A038505.
%Y A038518 Cf. A038519, A038520, A038521.
%K A038518 easy,nonn
%O A038518 0,5
%A A038518 _Frank Ruskey_