A058821 Dimensions of homogeneous subspaces of shuffle algebra over 6-letter alphabet (see A058766 for 2-letter case).

1, 6, 21, 146, 981, 6222, 38921, 239946, 1469826, 8957976, 54420339, 329815506, 1995387801, 12056025246, 72766743801, 438839319470, 2644790643216, 15930973595046, 95917737415956, 577288174746786, 3473350521083199, 20892333943230346, 125638899138654861

Offset

0,2

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.

Formula

For n >= 2, a(n) = 6^n - (1/n) * Sum_{d|n} A008683(n/d) * 6^d. - Sean A. Irvine, Aug 28 2022

a(n) = 6^n - A032164(n) for n >= 2. - Amiram Eldar, Aug 13 2023

Mathematica

a[n_] := 6^n - DivisorSum[n, MoebiusMu[n/#] * 6^# &] / n; a[0] = 1; a[1] = 6; Array[a, 23, 0] (* Amiram Eldar, Aug 13 2023 *)

Crossrefs

Cf. A000400, A008683, A032164, A058766.

Sequence in context: A081077 A093775 A318103 * A054366 A304264 A210443

Adjacent sequences: A058818 A058819 A058820 * A058822 A058823 A058824

Keyword

nonn

Author

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

Extensions

More terms from Sean A. Irvine, Aug 28 2022

Status

approved