A058822 a(0) = 1, a(1) = 7; for n>=2 a(n) is the number of degree-n monic reducible polynomials over GF(7), i.e., a(n) = 7^n - A001693(n).

1, 7, 28, 231, 1813, 13447, 98105, 705895, 5044501, 35869911, 254229409, 1797569767, 12687856601, 89436009607, 629778626473, 4431057410423, 31155872769301, 218946366105607, 1537946178052697, 10798953333511399, 75802652996855281, 531948441984119239, 3732101910100912537

Offset: 0

Author

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

Keywords

• nonn

Comments

Dimensions of homogeneous subspaces of shuffle algebra over 7-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. A000420, A001693, A058766.

Programs

Mathematica

a[n_] := 7^n - DivisorSum[n, MoebiusMu[n/#] * 7^# &] / n; a[0] = 1; a[1] = 7; Array[a, 23, 0] (* Amiram Eldar, Aug 13 2023 *)

PARI

a(n) = if (n<=1, 7^n, 7^n - sumdiv(n, d, moebius(d)*7^(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