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A058822
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a(0) = 1, a(1) = 7; for n>=2 a(n) is the number of degree-n monic reducible polynomials over GF(7), i.e., a(n) = 7^n - A001693(n).
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0
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1, 7, 28, 231, 1813, 13447, 98105, 705895, 5044501, 35869911, 254229409, 1797569767, 12687856601, 89436009607, 629778626473, 4431057410423, 31155872769301, 218946366105607, 1537946178052697, 10798953333511399, 75802652996855281, 531948441984119239, 3732101910100912537
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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 7-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_] := 7^n - DivisorSum[n, MoebiusMu[n/#] * 7^# &] / n; a[0] = 1; a[1] = 7; Array[a, 23, 0] (* Amiram Eldar, Aug 13 2023 *)
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PROG
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(PARI) a(n) = if (n<=1, 7^n, 7^n - sumdiv(n, d, moebius(d)*7^(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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