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A058766
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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).
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8
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1, 2, 3, 6, 13, 26, 55, 110, 226, 456, 925, 1862, 3761, 7562, 15223, 30586, 61456, 123362, 247612
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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.
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REFERENCES
| M. Lothaire, Combinatorics on words, Cambridge mathematical library, 1983, p. 126 (definition of shuffle algebra).
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EXAMPLE
| Degree 3: x uu x = 2 x^2, y uu y = 2 y^2, x uu y = xy + yx.
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CROSSREFS
| Cf. A001037.
Sequence in context: A079662 A007910 A052702 * A127601 A030038 A030040
Adjacent sequences: A058763 A058764 A058765 * A058767 A058768 A058769
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KEYWORD
| nonn
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AUTHOR
| Claude Lenormand (claude.lenormand(AT)free.fr), Jan 03 2001
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EXTENSIONS
| Better description from Sharon Sela (sharonsela(AT)hotmail.com), Feb 19 2002
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