A058822 - OEIS

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

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OFFSET

0,2

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).

LINKS

Table of n, a(n) for n=0..22.

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 *)

PROG

(PARI) a(n) = if (n<=1, 7^n, 7^n - sumdiv(n, d, moebius(d)*7^(n/d))/n); \\ Michel Marcus, Oct 30 2017

CROSSREFS

Cf. A000420, A001693, A058766.

Sequence in context: A224663 A203296 A355155 * A054369 A185360 A198028

Adjacent sequences: A058819 A058820 A058821 * A058823 A058824 A058825

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