|
Search: id:A042980
|
|
|
| A042980 |
|
Number of degree-n irreducible polynomials over GF(2) with trace = 0 and subtrace = 0. |
|
+0
5
|
|
| 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; listen)
|
|
|
OFFSET
|
1,6
|
|
|
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.
|
|
LINKS
|
F. Ruskey, Number of irreducible polynomials over GF(2) with given trace and subtrace
|
|
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)}.
|
|
CROSSREFS
|
Cf. A042979-A042982.
Cf. A074027-A074030.
Sequence in context: A050216 A037079 A101325 this_sequence A048290 A029939 A082198
Adjacent sequences: A042977 A042978 A042979 this_sequence A042981 A042982 A042983
|
|
KEYWORD
|
nonn,nice,easy
|
|
AUTHOR
|
Frank Ruskey (fruskey(AT)cs.uvic.ca)
|
|
|
Search completed in 0.002 seconds
|
