Lightly Documented Features

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(For In[1] see Setup)

In[2]:= ?NumberOfKnots
NumberOfKnots[n] returns the number of knots with n crossings. NumberOfKnots[n, Alternating|NonAlternating] returns the number of knots of the specified type.
In[3]:= NumberOfKnots[16, NonAlternating]
Out[3]= 1008906
In[4]:= ?AlternatingQ
AlternatingQ[D] returns True iff the knot/link diagram D is alternating.

Among the knots with up to 11 crossings, 564 are alternating and 238 are not:

In[5]:= Total[AlternatingQ /@ AllKnots[{0,11}]]
Out[5]= 238 False + 564 True