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A058819
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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).
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0
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1, 4, 10, 44, 196, 820, 3426, 14044, 57376, 233024, 943822, 3813004, 15379476, 61946644, 249262666, 1002159108, 4026535936, 16169288644, 64901742816, 260410648684, 1044536098828, 4188615725644, 16792541414866, 67309233561244, 269746853382816, 1080863910568960, 4330384259668126
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OFFSET
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0,2
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COMMENTS
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Dimensions of homogeneous subspaces of shuffle algebra over 4-letter alphabet (see A058766 for 2-letter case).
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REFERENCES
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M. Lothaire, Combinatorics on words, Cambridge mathematical library, 1983, p. 126 (definition of shuffle algebra).
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n) = if (n<=1, 4^n, 4^n - sumdiv(n, d, moebius(d)*4^(n/d))/n); \\ Michel Marcus, Oct 30 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Claude Lenormand (claude.lenormand(AT)free.fr), Jan 04 2001
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EXTENSIONS
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Better description from Sharon Sela (sharonsela(AT)hotmail.com), Feb 19 2002
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STATUS
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approved
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