

A038519


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


4



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
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OFFSET

0,4


LINKS



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.
a(n) = ((1i)^n + (1+i)^n + 2^n) / 4 for n>0.
a(n) = 2*a(n2) + 4*a(n3) 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(m2)+4*Self(m3):m in [1..33]]; // Marius A. Burtea, Aug 02 2019


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



