A058819 a(0) = 1, a(1) = 4; for n >= 2 a(n) is the number of degree-n monic reducible polynomials over GF(4), i.e., a(n) = 4^n - A027377(n).

1, 4, 10, 44, 196, 820, 3426, 14044, 57376, 233024, 943822, 3813004, 15379476, 61946644, 249262666, 1002159108, 4026535936, 16169288644, 64901742816, 260410648684, 1044536098828, 4188615725644, 16792541414866, 67309233561244, 269746853382816, 1080863910568960, 4330384259668126

Offset

0,2

Comments

Dimensions of homogeneous subspaces of shuffle algebra over 4-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..26.

Mathematica

a[n_] := 4^n - DivisorSum[n, MoebiusMu[n/#] * 4^# &] / n; a[0] = 1; a[1] = 4; Array[a, 27, 0] (* Amiram Eldar, Aug 13 2023 *)

Prog

(PARI) a(n) = if (n<=1, 4^n, 4^n - sumdiv(n, d, moebius(d)*4^(n/d))/n); \\ Michel Marcus, Oct 30 2017

Crossrefs

Cf. A000302, A027377, A058766.

Sequence in context: A149224 A149225 A122648 * A052394 A197627 A066229

Adjacent sequences: A058816 A058817 A058818 * A058820 A058821 A058822

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