A056268 Number of primitive (aperiodic) words of length n which contain exactly three different symbols.

0, 0, 6, 36, 150, 534, 1806, 5760, 18144, 55830, 171006, 518580, 1569750, 4732014, 14250450, 42844320, 128746950, 386615376, 1160688606, 3483582660, 10454059938, 31368305694, 94118013006, 282378679920, 847187946000, 2541662931990, 7625194813656, 22875982414740

Offset

1,3

References

M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Links

Table of n, a(n) for n=1..28.

Formula

a(n) = Sum_{d|n} mu(d)*A001117(n/d).

Prog

(PARI) f(n) = 3^n - 3*2^n + 3;
a(n) = sumdiv(n, d, moebius(d)*f(n/d)); \\ Michel Marcus, Mar 25 2022

Crossrefs

Cf. A000244, A001117, A008683, A054718.

Sequence in context: A181478 A223841 A210322 * A001117 A353664 A353774

Adjacent sequences: A056265 A056266 A056267 * A056269 A056270 A056271

Keyword

nonn

Author

Marks R. Nester

Extensions

a(11) and following corrected by Georg Fischer, Mar 24 2022

Status

approved