A054662 Number of monic irreducible polynomials over GF(5) with fixed nonzero trace.

1, 2, 8, 30, 125, 516, 2232, 9750, 43400, 195250, 887784, 4068740, 18780048, 87191964, 406901000, 1907343750, 8975758272, 42385503300, 200773540296, 953674218750, 4541306267856, 21674415838068, 103660251783288

Offset

1,2

Comments

Also number of 5-ary Lyndon words with trace 1 mod 5; trace 2 mod 5; trace 3 mod 5; trace 4 mod 5; also number of 5-ary Lyndon words of trace 1 over GF(5), trace 2 over GF(5); trace 3 over GF(5); trace 4 over GF(5).

Links

Table of n, a(n) for n=1..23.

F. Ruskey, Number of monic irreducible polynomials over GF(q) with given trace

F. Ruskey, Number of q-ary Lyndon words with given trace mod q

F. Ruskey, Number of Lyndon words over GF(q) with given trace

Crossrefs

Cf. A000048, A051841, A046211, A046209, A054661, etc.

Sequence in context: A074026 A054663 A150763 * A150764 A150765 A150766

Adjacent sequences: A054659 A054660 A054661 * A054663 A054664 A054665

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 18 2000

Extensions

More terms from James A. Sellers, Apr 19 2000

Status

approved