A056267 Number of primitive (aperiodic) words of length n which contain exactly two different symbols.

0, 2, 6, 12, 30, 54, 126, 240, 504, 990, 2046, 4020, 8190, 16254, 32730, 65280, 131070, 261576, 524286, 1047540, 2097018, 4192254, 8388606, 16772880, 33554400, 67100670, 134217216, 268419060, 536870910, 1073708010, 2147483646

Offset: 1

Author

Marks R. Nester

Keywords

• nonn

References

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

Crossrefs

Cf. A000079, A000918.

A027375 and A038199 are essentially the same sequence with different initial terms.

Programs

PARI

a(n) = sumdiv(n, d, moebius(d)*(2^(n/d) - 2)); \\ Michel Marcus, Jun 30 2019

Formula

a(n) = Sum_{d|n} mu(d)*A000918(n/d), n>0.

Extensions

Corrected and extended by Franklin T. Adams-Watters and T. D. Noe, Oct 25 2006