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A058818
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a(0) = 1, a(1) = 3; for n >= 2 a(n) is the number of degree-n monic reducible polynomials over GF(3), i.e., a(n) = 3^n - A027376(n).
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0
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1, 3, 6, 19, 63, 195, 613, 1875, 5751, 17499, 53169, 161043, 487221, 1471683, 4441485, 13392331, 40356711, 121543683, 365898261, 1101089811, 3312448137, 9962241251, 29954655861, 90049997139, 270661661541, 813397065075, 2444101819329, 7343167949235
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OFFSET
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0,2
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COMMENTS
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Dimensions of homogeneous subspaces of shuffle algebra over 3-letter alphabet (see A058766 for 2-letter case).
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REFERENCES
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M. Lothaire, Combinatorics on words, Cambridge mathematical library, 1983, p. 126 (definition of shuffle algebra).
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LINKS
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MATHEMATICA
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a[n_] := 3^n - DivisorSum[n, MoebiusMu[n/#] * 3^# &] / n; a[0] = 1; a[1] = 3; Array[a, 28, 0] (* Amiram Eldar, Aug 13 2023 *)
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PROG
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(PARI) a(n) = if (n<=1, 3^n, 3^n - sumdiv(n, d, moebius(d)*3^(n/d))/n); \\ Michel Marcus, Oct 30 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Claude Lenormand (claude.lenormand(AT)free.fr), Jan 04 2001
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EXTENSIONS
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Better description from Sharon Sela (sharonsela(AT)hotmail.com), Feb 19 2002
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STATUS
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approved
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