Geodesic
The Fermat Cubic, Elliptic Functions, Continued Fractions, and a Combinatorial Excursion
Séminaire lotharingien de combinatoire, Tome 54 (2006-2007)
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Elliptic functions considered by Dixon in the nineteenth century and related to Fermat's cubic, x3+y3=1, lead to a new set of continued fraction expansions with sextic numerators and cubic denominators. The functions and the fractions are pregnant with interesting combinatorics, including a special Pólya urn, a continuous-time branching process of the Yule type, as well as permutations satisfying various constraints that involve either parity of levels of elements or a repetitive pattern of order three. The combinatorial models are related to but different from models of elliptic functions earlier introduced by Viennot, Flajolet, Dumont, and Françon. 

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     author = {Eric van Fossen Conrad and Philippe Flajolet},
     title = {The {Fermat} {Cubic,} {Elliptic} {Functions,} {Continued} {Fractions,} and a {Combinatorial} {Excursion}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2006-2007},
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     url = {http://geodesic.mathdoc.fr/item/SLC_2006-2007_54_a6/}
}
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Eric van Fossen Conrad; Philippe Flajolet. The Fermat Cubic, Elliptic Functions, Continued Fractions, and a Combinatorial Excursion. Séminaire lotharingien de combinatoire, Tome 54 (2006-2007). http://geodesic.mathdoc.fr/item/SLC_2006-2007_54_a6/