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Search: id:A038518
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| A038518 |
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Number of elements of GF(2^n) with trace 0 and subtrace 0. |
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4
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| 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; listen)
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OFFSET
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0,5
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LINKS
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F. Ruskey, Number of irreducible polynomials over GF(2) with given trace and subtrace
F. Ruskey, Number of elements of GF(2^n) of given trace and subtrace
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FORMULA
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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
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MAPLE
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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)
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CROSSREFS
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Cf. A038503, A038505.
Cf. A038519, A038520, A038521.
Sequence in context: A085596 A107620 A058563 this_sequence A000976 A092297 A073096
Adjacent sequences: A038515 A038516 A038517 this_sequence A038519 A038520 A038521
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KEYWORD
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easy,nonn
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AUTHOR
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Frank Ruskey (fruskey(AT)cs.uvic.ca)
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