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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A058766 a(0) = 1, a(1) = 2; for n>=2 a(n) is the number of degree-n reducible polynomials over GF(2). 8
 1, 2, 3, 6, 13, 26, 55, 110, 226, 456, 925, 1862, 3761, 7562, 15223, 30586, 61456, 123362, 247612, 496694, 996199, 1997294, 4003747, 8023886, 16078346, 32212256, 64528069, 129246720, 258849061, 518358122, 1037951557, 2078209982, 4160751616 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Dimensions of homogeneous subspaces of shuffle algebra defined in the "Comments" line. Let x and y be two letters, m and m' any two words, e is the empty word of the free monoid generated by (x,y). Let uu denote the shuffle or Hurwitz product: xm uu ym' =x.(m uu ym') + y.(xm uu m'); of course, e is neutral. REFERENCES M. Lothaire, Combinatorics on words, Cambridge mathematical library, 1983, p. 126 (definition of shuffle algebra). LINKS FORMULA For n>=2, a(n) = 2^n - A001037(n). EXAMPLE Degree 3: x uu x = 2 x^2, y uu y = 2 y^2, x uu y = xy + yx. CROSSREFS Cf. A001037. Sequence in context: A007910 A293315 A052702 * A127601 A030038 A030040 Adjacent sequences:  A058763 A058764 A058765 * A058767 A058768 A058769 KEYWORD nonn AUTHOR Claude Lenormand (claude.lenormand(AT)free.fr), Jan 03 2001 EXTENSIONS Better description from Sharon Sela (sharonsela(AT)hotmail.com), Feb 19 2002 More terms from Max Alekseyev, Aug 24 2012 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.

Last modified September 27 12:30 EDT 2020. Contains 337380 sequences. (Running on oeis4.)