We define a language L to be an arbitrary subset of 
.
Associated to a language we have a power series 
in two variables
b and w where
and
is the number of words in L which involve exactly m copies
of the letter B and n copies of the letter 
consists of all words which do not involve
W then 
whenever n>0, and 
for every m
since there is exactly one word in the language of length m involving
no 
Thus
the power series is 
consists of all words in 
of length t where t is fixed, then
If we further specify that t=3 to give the language 
we have
In this case the power series collapse to being a polynomial expression,
since all save a finite number of coefficients vanish. Notice that
the coefficients here are drawn from a row of Pascal's triangle,
and another way of describing 
is 
To understand this,
think of + as being ``or'' and multiplication (juxtaposition) as being
``and then''. In this sense 
exactly describes
the 
Each word in 
is of the form:
B or W, then B or W, then B or 
consists of all words where
there are no juxtaposed Ws and no juxtaposed Bs then there
is one word in 
of length 0, the empty word, and exactly two
words of every other length. Thus 
The particular languages of interest in the investigation of snail venom are the ones satisfying the following five conditions.
Between at least one 
-th and 2i-th occurrence
of B, there must at least two consecutive occurrences of 
The language S specified by the first three conditions are all possible words associated with snail venom. The language defined by all five these conditions are the so-called inaccessible words, and are exactly those which do not admit of synthesis by a specific manufacturing process.
The language S is defined by conditions
and 
Let 
The definition of 
yields that
or more formally
If you wish to see you many words there are in
this language of length 30 and involving 8 occurrences of
B (and so 22 occurrences of W) you look at the coefficient
of 
and this is precisely the coefficient of 
in 
This can be determined in a trice by almost any computer
algebra system (AXIOM, MAPLE, REDUCE etc).
Now we proceed to the main calculation, where we also impose conditions
and 
and are particularly interested in the cases where
there are 4, 6 and 8 occurrences of B, and when the word
lengths does not happen to exceed 30. This final constraint can
be imposed at the very end of the calculations by truncating
the appropriate polynomial if necessary.