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You can use different weight functions on such a set. Three
candidates are: *the number of *0's *the number of
*1's, and *the total number of 0's or 1's* (nops).

The generating function which makes use of all of these weights is:

The closed form representation of this generating function (as
obtained directly from the construction marking 0's and 1's) is

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** Next:** A Validity Check
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