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%I #14 Aug 13 2023 02:47:33
%S 1,7,28,231,1813,13447,98105,705895,5044501,35869911,254229409,
%T 1797569767,12687856601,89436009607,629778626473,4431057410423,
%U 31155872769301,218946366105607,1537946178052697,10798953333511399,75802652996855281,531948441984119239,3732101910100912537
%N 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).
%C Dimensions of homogeneous subspaces of shuffle algebra over 7-letter alphabet (see A058766 for 2-letter case).
%D M. Lothaire, Combinatorics on words, Cambridge mathematical library, 1983, p. 126 (definition of shuffle algebra).
%t 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 *)
%o (PARI) a(n) = if (n<=1, 7^n, 7^n - sumdiv(n, d, moebius(d)*7^(n/d))/n); \\ _Michel Marcus_, Oct 30 2017
%Y Cf. A000420, A001693, A058766.
%K nonn
%O 0,2
%A Claude Lenormand (claude.lenormand(AT)free.fr), Jan 04 2001
%E Better description from Sharon Sela (sharonsela(AT)hotmail.com), Feb 19 2002
%E More terms from _Michel Marcus_, Oct 30 2017
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