|
Search: id:A042981
|
|
|
| A042981 |
|
Number of degree-n irreducible polynomials over GF(2) with trace = 1 and subtrace = 0. |
|
+0
3
|
|
| 1, 0, 1, 1, 1, 3, 4, 8, 15, 24, 48, 85, 155, 297, 541, 1024, 1935, 3626, 6912, 13107, 24940, 47709, 91136, 174760, 335626, 645120, 1242904, 2396745, 4627915, 8948385, 17317888, 33554432
(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 = 2 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: A026654 A104370 A033854 this_sequence A007486 A027977 A165438
Adjacent sequences: A042978 A042979 A042980 this_sequence A042982 A042983 A042984
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Frank Ruskey (fruskey(AT)cs.uvic.ca)
|
|
|
Search completed in 0.002 seconds
|
