login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054660 Number of monic irreducible polynomials over GF(4) with fixed nonzero trace. 10
1, 2, 5, 16, 51, 170, 585, 2048, 7280, 26214, 95325, 349520, 1290555, 4793490, 17895679, 67108864, 252645135, 954437120, 3616814565, 13743895344, 52357696365, 199911205050, 764877654105, 2932031006720, 11258999068416 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also number of Lyndon words of length n with trace 1 over GF(4).

Let x = RootOf( z^2+z+1 ) and y = 1+x. Also number of Lyndon words of length n with trace x over GF(4). Also number of Lyndon words of length n with trace y over GF(4).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..1000

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

FORMULA

From Seiichi Manyama, Mar 11 2018: (Start)

a(n) = A000048(2*n) = (1/(4*n)) * Sum_{odd d divides n} mu(d)*4^(n/d), where mu is the Möbius function A008683.

a(n+1) = A300628(n,n) for n >= 0. (End)

EXAMPLE

a(3; y)=5 since the five 4-ary Lyndon words of trace y and length 3 are { 00y, 01x, 0x1, 11y, xxy }.

CROSSREFS

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

Cf. A008683, A054661, A074025, A300628.

Sequence in context: A148386 A148387 A121651 * A231296 A148388 A148389

Adjacent sequences:  A054657 A054658 A054659 * A054661 A054662 A054663

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Apr 18 2000

EXTENSIONS

More terms from James A. Sellers, Apr 19 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 27 15:27 EDT 2020. Contains 338035 sequences. (Running on oeis4.)