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A058818 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).

%I A058818 #16 Aug 13 2023 02:16:48
%S A058818 1,3,6,19,63,195,613,1875,5751,17499,53169,161043,487221,1471683,
%T A058818 4441485,13392331,40356711,121543683,365898261,1101089811,3312448137,
%U A058818 9962241251,29954655861,90049997139,270661661541,813397065075,2444101819329,7343167949235
%N A058818 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).
%C A058818 Dimensions of homogeneous subspaces of shuffle algebra over 3-letter alphabet (see A058766 for 2-letter case).
%D A058818 M. Lothaire, Combinatorics on words, Cambridge mathematical library, 1983, p. 126 (definition of shuffle algebra).
%t A058818 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 *)
%o A058818 (PARI) a(n) = if (n<=1, 3^n, 3^n - sumdiv(n, d, moebius(d)*3^(n/d))/n); \\ _Michel Marcus_, Oct 30 2017
%Y A058818 Cf. A027376, A058766.
%K A058818 nonn
%O A058818 0,2
%A A058818 Claude Lenormand (claude.lenormand(AT)free.fr), Jan 04 2001
%E A058818 Better description from Sharon Sela (sharonsela(AT)hotmail.com), Feb 19 2002
%E A058818 a(16)-a(27) from _Alois P. Heinz_, Nov 25 2016