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A042980
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Number of degree-n irreducible polynomials over GF(2) with trace = 0 and subtrace = 0.
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4
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1, 0, 0, 1, 1, 2, 5, 6, 15, 24, 45, 85, 155, 288, 550, 1008, 1935, 3626, 6885, 13107, 24940, 47616, 91225, 174590, 335626, 645120, 1242600, 2396745, 4627915, 8947294, 17318945, 33552384
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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REFERENCES
| 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
| F. Ruskey, Number of irreducible polynomials over GF(2) with given trace and subtrace
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FORMULA
| a(n) = Sum{ L(n, k) : n+k = 0 mod 4}, where L(n, k) = Sum{ mu(d)*{n/d choose k/d}: d|gcd(n, k)}.
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CROSSREFS
| Cf. A042979-A042982.
Cf. A074027-A074030.
Sequence in context: A193405 A037079 A101325 * A048290 A029939 A082198
Adjacent sequences: A042977 A042978 A042979 * A042981 A042982 A042983
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Frank Ruskey (ruskey(AT)cs.uvic.ca)
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