A058824 a(0) = 1, a(1) = 9; for n >= 2 a(n) is the number of degree-n monic reducible polynomials over GF(9), i.e., a(n) = 9^n - A027381(n).

1, 9, 45, 489, 4941, 47241, 443001, 4099689, 37666701, 344373849, 3138111873, 28528236009, 258893786601, 2346337687689, 21242736192681, 192165056625657, 1737206429739021, 15696171011450889, 141756044468718681, 1279754258848097769, 11549782186278421905, 104208561077631046089

Offset: 0

Author

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

Keywords

• nonn

Comments

Dimensions of homogeneous subspaces of shuffle algebra over 9-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. A001019, A027381, A058766.

Programs

Mathematica

a[n_] := 9^n - DivisorSum[n, MoebiusMu[n/#] * 9^# &] / n; a[0] = 1; a[1] = 9; Array[a, 22, 0] (* Amiram Eldar, Aug 13 2023 *)

PARI

a(n) = if (n<=1, 9^n, 9^n - sumdiv(n, d, moebius(d)*9^(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