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A058819 a(0) = 1, a(1) = 4; for n >= 2 a(n) is the number of degree-n monic reducible polynomials over GF(4), i.e., a(n) = 4^n - A027377(n).

%I A058819 #14 Aug 13 2023 02:48:15
%S A058819 1,4,10,44,196,820,3426,14044,57376,233024,943822,3813004,15379476,
%T A058819 61946644,249262666,1002159108,4026535936,16169288644,64901742816,
%U A058819 260410648684,1044536098828,4188615725644,16792541414866,67309233561244,269746853382816,1080863910568960,4330384259668126
%N A058819 a(0) = 1, a(1) = 4; for n >= 2 a(n) is the number of degree-n monic reducible polynomials over GF(4), i.e., a(n) = 4^n - A027377(n).
%C A058819 Dimensions of homogeneous subspaces of shuffle algebra over 4-letter alphabet (see A058766 for 2-letter case).
%D A058819 M. Lothaire, Combinatorics on words, Cambridge mathematical library, 1983, p. 126 (definition of shuffle algebra).
%t A058819 a[n_] := 4^n - DivisorSum[n, MoebiusMu[n/#] * 4^# &] / n; a[0] = 1; a[1] = 4; Array[a, 27, 0] (* _Amiram Eldar_, Aug 13 2023 *)
%o A058819 (PARI) a(n) = if (n<=1, 4^n, 4^n - sumdiv(n, d, moebius(d)*4^(n/d))/n); \\ _Michel Marcus_, Oct 30 2017
%Y A058819 Cf. A000302, A027377, A058766.
%K A058819 nonn
%O A058819 0,2
%A A058819 Claude Lenormand (claude.lenormand(AT)free.fr), Jan 04 2001
%E A058819 Better description from Sharon Sela (sharonsela(AT)hotmail.com), Feb 19 2002
%E A058819 More terms from _Michel Marcus_, Oct 30 2017