A058820 a(0) = 1, a(1) = 5; for n >= 2 a(n) is the number of degree-n monic reducible polynomials over GF(5), i.e., a(n) = 5^n - A001692(n).

1, 5, 15, 85, 475, 2501, 13045, 66965, 341875, 1736125, 8789377, 44389205, 223796925, 1126802885, 5667555805, 28483073133, 143051171875, 718060661765, 3602769749125, 18069618626645, 90599060546905, 454130626863845, 2275813711825285, 11402627696161685, 57121117919938125

Offset: 0

Author

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

Keywords

• nonn

Comments

Dimensions of homogeneous subspaces of shuffle algebra over 5-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. A000351, A001692, A058766.

Programs

Mathematica

a[n_] := 5^n - DivisorSum[n, MoebiusMu[n/#] * 5^# &] / n; a[0] = 1; a[1] = 5; Array[a, 25, 0] (* Amiram Eldar, Aug 13 2023 *)

PARI

a(n) = if (n<=1, 5^n, 5^n - sumdiv(n, d, moebius(d)*5^(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