%I
%S 1,2,3,6,13,26,55,110,226,456,925,1862,3761,7562,15223,30586,61456,
%T 123362,247612,496694,996199,1997294,4003747,8023886,16078346,
%U 32212256,64528069,129246720,258849061,518358122,1037951557,2078209982,4160751616
%N a(0) = 1, a(1) = 2; for n>=2 a(n) is the number of degreen reducible polynomials over GF(2).
%C Dimensions of homogeneous subspaces of shuffle algebra defined in the "Comments" line.
%C 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.
%D M. Lothaire, Combinatorics on words, Cambridge mathematical library, 1983, p. 126 (definition of shuffle algebra).
%F For n>=2, a(n) = 2^n  A001037(n).
%e Degree 3: x uu x = 2 x^2, y uu y = 2 y^2, x uu y = xy + yx.
%Y Cf. A001037.
%K nonn
%O 0,2
%A Claude Lenormand (claude.lenormand(AT)free.fr), Jan 03 2001
%E Better description from Sharon Sela (sharonsela(AT)hotmail.com), Feb 19 2002
%E More terms from _Max Alekseyev_, Aug 24 2012
