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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). 9
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.
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A007910 A293315 A052702 * A127601 A030038 A030040
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

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)