[seqfan] A124677 vs A075099
Benoît Jubin
benoit.jubin at gmail.com
Sun Jan 25 02:19:15 CET 2009
The sequences A075099 and A124677 have the same definition but not the
same values.
I would leave A075099 unchanged, that is:
%N A075099 Minimal total number of multiplications needed to generate
all words of length n in the free monoid on two generators.
and write for the other:
%N A124677 Minimal total number of multiplications by one-letter words
needed to generate all words of length n in the free monoid on two
generators, considering that a one-letter word needs one
multiplication
(as far as I understand it)
Also, in %e A124677, the expression a(3)=11 should be replaced by a(3)=13.
Also, for
%E A075100 Shouldn't a(2) = 2 ? Shouldn't a(3) = 5, because we need x,
y, xx, xy, yy ? I'm confused! - njas, Dec 25 2006
I think the confusion comes from the fact that njas counts the
one-letter words, so obtains always the written value plus 2.
I think njas's way of counting is preferable, so the terms should be
changed accordingly.
Actually, maybe we should replace "free monoid" by "free semigroup" in
the definitions of A075099 and A075100 (which both have offset 1, and
not 0) to make it clearer.
Benoit
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