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A058823
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).
0
1, 8, 36, 344, 3088, 26216, 218548, 1797560, 14680576, 119304704, 966370924, 7809031448, 62992875856, 507466905128, 4083900481540, 32838747285128, 263882791714816, 2119341001115528, 17013598599759616, 136530178177126616, 1095275429430191920, 8784163844623695896
OFFSET
0,2
COMMENTS
Dimensions of homogeneous subspaces of shuffle algebra over 8-letter alphabet (see A058766 for 2-letter case).
REFERENCES
M. Lothaire, Combinatorics on words, Cambridge mathematical library, 1983, p. 126 (definition of shuffle algebra).
MATHEMATICA
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 *)
PROG
(PARI) a(n) = if (n<=1, 8^n, 8^n - sumdiv(n, d, moebius(d)*8^(n/d))/n); \\ Michel Marcus, Oct 30 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Claude Lenormand (claude.lenormand(AT)free.fr), Jan 04 2001
EXTENSIONS
Better description from Sharon Sela (sharonsela(AT)hotmail.com), Feb 19 2002
More terms from Michel Marcus, Oct 30 2017
STATUS
approved