Nonalternating Knot
A knot which is not alternating. Unlike alternating knots, flype moves are not sufficient to pass between all minimal diagrams of a given nonalternating knot (Hoste et al. 1998). In fact, Thistlethwaite used 13 different moves in generating a list of 16-crossing alternating knots (Hoste et al. 1998), and still had 
duplicates out of a list of 
knots (Hoste et al. 1998).
The numbers of nonalternating knots with 
, 2, ... crossings are 0, 0, 0, 0, 0, 0, 0, 3, 8, 42, 185, 888, ... (OEIS A051763), the first few of which are 
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REFERENCES:
Hoste, J.; Thistlethwaite, M.; and Weeks, J. "The First 
Knots." Math. Intell. 20, 33-48, Fall 1998.
Sloane, N. J. A. Sequence A051763 in "The On-Line Encyclopedia of Integer Sequences."
