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 A058822 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). 0
 1, 7, 28, 231, 1813, 13447, 98105, 705895, 5044501, 35869911, 254229409, 1797569767, 12687856601, 89436009607, 629778626473, 4431057410423, 31155872769301, 218946366105607, 1537946178052697, 10798953333511399, 75802652996855281, 531948441984119239, 3732101910100912537 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Dimensions of homogeneous subspaces of shuffle algebra over 7-letter alphabet (see A058766 for 2-letter case). REFERENCES M. Lothaire, Combinatorics on words, Cambridge mathematical library, 1983, p. 126 (definition of shuffle algebra). LINKS Table of n, a(n) for n=0..22. MATHEMATICA 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 *) PROG (PARI) a(n) = if (n<=1, 7^n, 7^n - sumdiv(n, d, moebius(d)*7^(n/d))/n); \\ Michel Marcus, Oct 30 2017 CROSSREFS Cf. A000420, A001693, A058766. Sequence in context: A224663 A203296 A355155 * A054369 A185360 A198028 Adjacent sequences: A058819 A058820 A058821 * A058823 A058824 A058825 KEYWORD nonn AUTHOR Claude Lenormand (claude.lenormand(AT)free.fr), Jan 04 2001 EXTENSIONS Better description from Sharon Sela (sharonsela(AT)hotmail.com), Feb 19 2002 More terms from Michel Marcus, Oct 30 2017 STATUS approved

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Last modified December 10 23:37 EST 2023. Contains 367717 sequences. (Running on oeis4.)