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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). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

LINKS

Table of n, a(n) for n=0..27.

PROG

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

CROSSREFS

Cf. A027376, A058766.

Sequence in context: A052393 A024607 A186022 * A184937 A215817 A269306

Adjacent sequences:  A058815 A058816 A058817 * A058819 A058820 A058821

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

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

STATUS

approved

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Last modified December 4 09:10 EST 2021. Contains 349484 sequences. (Running on oeis4.)