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).

1, 8, 36, 344, 3088, 26216, 218548, 1797560, 14680576, 119304704, 966370924, 7809031448, 62992875856, 507466905128, 4083900481540, 32838747285128, 263882791714816, 2119341001115528, 17013598599759616, 136530178177126616, 1095275429430191920, 8784163844623695896

Offset: 0

Author

Claude Lenormand (claude.lenormand(AT)free.fr), Jan 04 2001

Keywords

• nonn

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).

Crossrefs

Cf. A001018, A027380, A058766.

Programs

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 *)

PARI

a(n) = if (n<=1, 8^n, 8^n - sumdiv(n, d, moebius(d)*8^(n/d))/n); \\ Michel Marcus, Oct 30 2017

Extensions

Better description from Sharon Sela (sharonsela(AT)hotmail.com), Feb 19 2002

More terms from Michel Marcus, Oct 30 2017