Search: id:A058766
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%I A058766
%S A058766 1,2,3,6,13,26,55,110,226,456,925,1862,3761,7562,15223,30586,61456,
%T A058766 123362,247612
%N A058766 a(0) = 1, a(1) = 2; for n>=2 a(n) is the number of degree-n reducible 
               polynomials over GF(2), i.e. a(n) = 2^n - A001037(n).
%C A058766 Dimensions of homogeneous subspaces of shuffle algebra defined in the 
               "Comments" line.
%C A058766 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 A058766 M. Lothaire, Combinatorics on words, Cambridge mathematical library, 
               1983, p. 126 (definition of shuffle algebra).
%e A058766 Degree 3: x uu x = 2 x^2, y uu y = 2 y^2, x uu y = xy + yx.
%Y A058766 Cf. A001037.
%Y A058766 Sequence in context: A079662 A007910 A052702 this_sequence A127601 A030038 
               A030040
%Y A058766 Adjacent sequences: A058763 A058764 A058765 this_sequence A058767 A058768 
               A058769
%K A058766 nonn
%O A058766 0,2
%A A058766 Claude Lenormand (claude.lenormand(AT)free.fr), Jan 03 2001
%E A058766 Better description from Sharon Sela (sharonsela(AT)hotmail.com), Feb 
               19 2002

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