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 A038518 Number of elements of GF(2^n) with trace 0 and subtrace 0. 5
 0, 1, 1, 1, 6, 6, 16, 36, 56, 136, 256, 496, 1056, 2016, 4096, 8256, 16256, 32896, 65536, 130816, 262656, 523776, 1048576, 2098176, 4192256, 8390656, 16777216, 33550336, 67117056, 134209536, 268435456, 536887296, 1073709056, 2147516416 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 F. Ruskey, Number of irreducible polynomials over GF(2) with given trace and subtrace F. Ruskey, Number of elements of GF(2^n) with given trace and subtrace Index entries for linear recurrences with constant coefficients, signature (0,2,4). FORMULA C(n, r+0)+C(n, r+4)+C(n, r+8)+... where r = 0 if n odd, r = 2 if n even. G.f.: (-x^3+x^2+x)/[(1-2x)(1+2x+2x^2)]. 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 a(n) = 2*a(n-2) + 4*a(n-3) for n>3. - Colin Barker, Aug 02 2019 MAPLE 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 MATHEMATICA LinearRecurrence[{0, 2, 4}, {0, 1, 1, 1}, 40] (* Harvey P. Dale, Mar 31 2020 *) PROG (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 CROSSREFS Cf. A038503, A038505. Cf. A038519, A038520, A038521. Sequence in context: A315813 A168460 A315814 * A151724 A335795 A315815 Adjacent sequences: A038515 A038516 A038517 * A038519 A038520 A038521 KEYWORD easy,nonn AUTHOR Frank Ruskey STATUS approved

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Last modified December 8 13:46 EST 2023. Contains 367679 sequences. (Running on oeis4.)