login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A062692 Number of irreducible polynomials over F_2 of degree at most n. 8
2, 3, 5, 8, 14, 23, 41, 71, 127, 226, 412, 747, 1377, 2538, 4720, 8800, 16510, 31042, 58636, 111013, 210871, 401428, 766150, 1465020, 2807196, 5387991, 10358999, 19945394, 38458184, 74248451, 143522117, 277737797, 538038783, 1043325198 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number of binary pre-necklaces of length n. - Joerg Arndt, Jul 20 2013

REFERENCES

Peter Burcsi, G Fici, Z Lipták, F Ruskey, J Sawada, On prefix normal words and prefix normal forms, Preprint, 2016; http://www.cis.uoguelph.ca/~sawada/papers/pnf.pdf

Hicks, Kenneth H.; Mullen, Gary L.; and Sato, Ikuro, Distribution of irreducible polynomials over F_2, in Finite Fields with Applications to Coding Theory, Cryptography and Related Areas (Oaxaca, 2001), 177-186, Springer, Berlin, 2002.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..3320

G. Fici and Zs. Lipták, On Prefix Normal Words.

G. Fici and Zs. Lipták, On Prefix Normal Words, Developments in Language Theory 2011, Lecture Notes in Computer Science 6795, 228-238.

M. Waldschmidt, Lectures on Multiple Zeta Values, IMSC 2011.

FORMULA

a(n) = Sum_{m=1..n} 1/m sum_{d | m } mu(d)*2^{m/d}.

MAPLE

with(numtheory):for n from 1 to 113 do sum3 := 0:for m from 1 to n do sum2 := 0:a := divisors(m):for h from 1 to nops(a) do sum2 := sum2+mobius(a[h])*2^(m/a[h]):end do:sum3 := sum3+sum2/m:end do:s[n] := sum3:end do:q := seq(s[j], j=1..113);

MATHEMATICA

a[n_] := Sum[1/m DivisorSum[m, MoebiusMu[#]*2^(m/#)&], {m, 1, n}]; Array[a, 34] (* Jean-François Alcover, Dec 07 2015 *)

PROG

(PARI) a(n)=sum(m=1, n, 1/m* sumdiv(m, d, moebius(d)*2^(m/d) ) ); /* Joerg Arndt, Jul 04 2011 */

CROSSREFS

Partial sums of A001037.

a(n) = A091226(2^(n+1)). Cf. A014580, A091231.

Equals A001036 + 1.

Column k=2 of A143328. - Alois P. Heinz, Jul 20 2013

Sequence in context: A191794 A191388 A194850 * A182024 A086661 A018154

Adjacent sequences:  A062689 A062690 A062691 * A062693 A062694 A062695

KEYWORD

nonn,easy

AUTHOR

Gary L Mullen (mullen(AT)math.psu.edu), Jul 04 2001

EXTENSIONS

More terms from Sascha Kurz, Mar 25 2002

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 16 18:57 EST 2017. Contains 296092 sequences.