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Search: id:A042979
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| A042979 |
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Number of degree-n irreducible polynomials over GF(2) with trace = 0 and subtrace = 1. |
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+0
10
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| 0, 0, 1, 0, 2, 2, 4, 8, 13, 24, 48, 80, 160, 288, 541, 1024, 1920, 3626, 6912, 13056, 24989, 47616, 91136, 174760, 335462, 645120, 1242904, 2396160, 4628480, 8947294, 17317888, 33554432
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OFFSET
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1,5
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REFERENCES
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K. Cattell, C.R. Miers, F. Ruskey, J. Sawada and M. Serra, "The Number of Irreducible Polynomials over GF(2) with Given Trace and Subtrace", J. Comb. Math. and Comb. Comp., 47 (2003) 31-64.
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LINKS
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F. Ruskey, Number of irreducible polynomials over GF(2) with given trace and subtrace
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FORMULA
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a(n) = Sum{ L(n, k) : n+k = 1 mod 4}, where L(n, k) = Sum{ mu(d)*{n/d choose k/d} : d|GCD(n, k)}
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CROSSREFS
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Cf. A042979-A042982.
Cf. A074027-A074030.
Sequence in context: A039941 A104700 A036761 this_sequence A000018 A075126 A098788
Adjacent sequences: A042976 A042977 A042978 this_sequence A042980 A042981 A042982
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KEYWORD
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nonn
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AUTHOR
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Frank Ruskey (fruskey(AT)cs.uvic.ca)
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