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%I #14 Aug 13 2023 02:47:22
%S 1,8,36,344,3088,26216,218548,1797560,14680576,119304704,966370924,
%T 7809031448,62992875856,507466905128,4083900481540,32838747285128,
%U 263882791714816,2119341001115528,17013598599759616,136530178177126616,1095275429430191920,8784163844623695896
%N a(0) = 1, a(1) = 8; for n >= 2 a(n) is the number of degree-n monic reducible polynomials over GF(8), i.e., a(n) = 8^n - A027380(n).
%C Dimensions of homogeneous subspaces of shuffle algebra over 8-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_] := 8^n - DivisorSum[n, MoebiusMu[n/#] * 8^# &] / n; a[0] = 1; a[1] = 8; Array[a, 22, 0] (* _Amiram Eldar_, Aug 13 2023 *)
%o (PARI) a(n) = if (n<=1, 8^n, 8^n - sumdiv(n, d, moebius(d)*8^(n/d))/n); \\ _Michel Marcus_, Oct 30 2017
%Y Cf. A001018, A027380, 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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