Benoit Jubin (Jan 24 2009) suggests replacing "monoid" in the definition by "semigroup".
I believe a(2n) = a(n) + 2^(2n). I guess a(7) = 156.
Table of n, a(n) for n=1..6.
a(3)=11 because each of xxx,xxy,xyx,xyy,yxx,yxy,yyx,yyy can be obtained in one step from xx,xy,yy and it takes three multiplications to produce xx, xy, yy.
Cf. A075100, A124677 (another version).
Sequence in context: A038413 A008174 A008262 * A240784 A240155 A161975
Adjacent sequences: A075096 A075097 A075098 * A075100 A075101 A075102
Colin Mallows, Aug 31 2002