A058818 a(0) = 1, a(1) = 3; for n >= 2 a(n) is the number of degree-n monic reducible polynomials over GF(3), i.e., a(n) = 3^n - A027376(n).

1, 3, 6, 19, 63, 195, 613, 1875, 5751, 17499, 53169, 161043, 487221, 1471683, 4441485, 13392331, 40356711, 121543683, 365898261, 1101089811, 3312448137, 9962241251, 29954655861, 90049997139, 270661661541, 813397065075, 2444101819329, 7343167949235

Offset: 0

Author

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

Keywords

• nonn

Comments

Dimensions of homogeneous subspaces of shuffle algebra over 3-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. A027376, A058766.

Programs

Mathematica

a[n_] := 3^n - DivisorSum[n, MoebiusMu[n/#] * 3^# &] / n; a[0] = 1; a[1] = 3; Array[a, 28, 0] (* Amiram Eldar, Aug 13 2023 *)

PARI

a(n) = if (n<=1, 3^n, 3^n - sumdiv(n, d, moebius(d)*3^(n/d))/n); \\ Michel Marcus, Oct 30 2017

Extensions

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

a(16)-a(27) from Alois P. Heinz, Nov 25 2016