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A038520 Number of elements of GF(2^n) with trace 1 and subtrace 0. 4
0, 1, 0, 3, 4, 6, 20, 28, 64, 136, 240, 528, 1024, 2016, 4160, 8128, 16384, 32896, 65280, 131328, 262144, 523776, 1049600, 2096128, 4194304, 8390656, 16773120, 33558528, 67108864, 134209536, 268451840, 536854528, 1073741824 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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

a(n) = C(n, r+0)+C(n, r+4)+C(n, r+8)+... where r = 1 if n odd, r = 3 if n even.

a(n) = 2*a(n-2) + 4*a(n-3), n > 3. - Paul Curtz, Feb 06 2008

From Colin Barker, Aug 02 2019: (Start)

G.f.: x*(1 + x^2) / ((1 - 2*x)*(1 + 2*x + 2*x^2)).

a(n) = (2^n + i*((-1-i)^n - (-1+i)^n)) / 4 for n>0, where i=sqrt(-1).

(End)

MATHEMATICA

LinearRecurrence[{0, 2, 4}, {0, 1, 0, 3}, 40] (* Harvey P. Dale, Oct 15 2017 *)

PROG

(PARI) concat(0, Vec(x*(1 + x^2) / ((1 - 2*x)*(1 + 2*x + 2*x^2)) + O(x^40))) \\ Colin Barker, Aug 02 2019

CROSSREFS

Cf. A038504, A000749, A038518, A038519, A038521.

Sequence in context: A066732 A304679 A265735 * A294990 A081888 A306493

Adjacent sequences:  A038517 A038518 A038519 * A038521 A038522 A038523

KEYWORD

easy,nonn

AUTHOR

Frank Ruskey

STATUS

approved

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Last modified May 12 20:41 EDT 2021. Contains 343829 sequences. (Running on oeis4.)