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%I #13 Aug 13 2023 02:47:53
%S 1,6,21,146,981,6222,38921,239946,1469826,8957976,54420339,329815506,
%T 1995387801,12056025246,72766743801,438839319470,2644790643216,
%U 15930973595046,95917737415956,577288174746786,3473350521083199,20892333943230346,125638899138654861
%N Dimensions of homogeneous subspaces of shuffle algebra over 6-letter alphabet (see A058766 for 2-letter case).
%D M. Lothaire, Combinatorics on words, Cambridge mathematical library, 1983, p. 126 (definition of shuffle algebra).
%F For n >= 2, a(n) = 6^n - (1/n) * Sum_{d|n} A008683(n/d) * 6^d. - _Sean A. Irvine_, Aug 28 2022
%F a(n) = 6^n - A032164(n) for n >= 2. - _Amiram Eldar_, Aug 13 2023
%t a[n_] := 6^n - DivisorSum[n, MoebiusMu[n/#] * 6^# &] / n; a[0] = 1; a[1] = 6; Array[a, 23, 0] (* _Amiram Eldar_, Aug 13 2023 *)
%Y Cf. A000400, A008683, A032164, A058766.
%K nonn
%O 0,2
%A Claude Lenormand (claude.lenormand(AT)free.fr), Jan 04 2001
%E More terms from _Sean A. Irvine_, Aug 28 2022
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