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

0,2

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).

Links

Table of n, a(n) for n=0..21.

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 *)

Prog

(PARI) a(n) = if (n<=1, 9^n, 9^n - sumdiv(n, d, moebius(d)*9^(n/d))/n); \\ Michel Marcus, Oct 30 2017

Crossrefs

Cf. A001019, A027381, A058766.

Sequence in context: A230063 A009432 A145757 * A244302 A177742 A322892

Adjacent sequences: A058821 A058822 A058823 * A058825 A058826 A058827

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