From Knot Atlas
(For In[1] see Setup)
| In[1]:=
| ?NumberOfKnots
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| NumberOfKnots[n] returns the number of knots with n crossings.
NumberOfKnots[n, Alternating|NonAlternating] returns the number of knots of the specified type.
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In[2]:=
| NumberOfKnots[16, NonAlternating]
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Out[2]=
| 1008906
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| In[3]:=
| ?AlternatingQ
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| AlternatingQ[D] returns True iff the knot/link diagram D is alternating.
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Among the knots with up to 11 crossings, 564 are alternating and 238 are not:
In[4]:=
| Total[AlternatingQ /@ AllKnots[{0,11}]]
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Out[4]=
| 238 False + 564 True
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