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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
OFFSET
0,4
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
KEYWORD
easy,nonn
AUTHOR
STATUS
approved