This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A058766 #11 Aug 13 2023 02:48:29 %S A058766 1,2,3,6,13,26,55,110,226,456,925,1862,3761,7562,15223,30586,61456, %T A058766 123362,247612,496694,996199,1997294,4003747,8023886,16078346, %U A058766 32212256,64528069,129246720,258849061,518358122,1037951557,2078209982,4160751616 %N A058766 a(0) = 1, a(1) = 2; for n>=2 a(n) is the number of degree-n reducible polynomials over GF(2). %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). %F A058766 For n>=2, a(n) = 2^n - A001037(n). %e A058766 Degree 3: x uu x = 2 x^2, y uu y = 2 y^2, x uu y = xy + yx. %t A058766 a[n_] := 2^n - DivisorSum[n, MoebiusMu[n/#] * 2^# &] / n; a[0] = 1; a[1] = 2; Array[a, 33, 0] (* _Amiram Eldar_, Aug 13 2023 *) %Y A058766 Cf. A000079, A001037. %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 %E A058766 More terms from _Max Alekseyev_, Aug 24 2012