A038519 Number of elements of GF(2^n) with trace 0 and subtrace 1.

1, 0, 1, 3, 2, 10, 16, 28, 72, 120, 256, 528, 992, 2080, 4096, 8128, 16512, 32640, 65536, 131328, 261632, 524800, 1048576, 2096128, 4196352, 8386560, 16777216, 33558528, 67100672, 134225920, 268435456, 536854528, 1073774592

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 = 2 if n odd, r = 0 if n even.

From Colin Barker, Aug 02 2019: (Start)

G.f.: (1 - x^2 - x^3) / ((1 - 2*x)*(1 + 2*x + 2*x^2)). - Creighton Dement, Apr 29 2005, corrected by Colin Barker, Aug 02 2019

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

a(n) = 2*a(n-2) + 4*a(n-3) for n>3.

(End)

Prog

(PARI) Vec((1 - x^2 - x^3) / ((1 - 2*x)*(1 + 2*x + 2*x^2)) + O(x^40)) \\ Colin Barker, Aug 02 2019
(Magma) I:=[1, 0, 1, 3]; [m le 4 select I[m] else 2*Self(m-2)+4*Self(m-3):m in [1..33]]; // Marius A. Burtea, Aug 02 2019

Crossrefs

Cf. A038503, A038505, A038518, A038520, A038521.

Sequence in context: A025520 A099946 A011953 * A192617 A082219 A034461

Adjacent sequences: A038516 A038517 A038518 * A038520 A038521 A038522

Keyword

easy,nonn

Author

Frank Ruskey

Status

approved