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A058766 a(0) = 1, a(1) = 2; for n>=2 a(n) is the number of degree-n reducible polynomials over GF(2). 8

%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 degree-n 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

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Last modified October 25 19:28 EDT 2020. Contains 338012 sequences. (Running on oeis4.)