Geodesic
The Kruskal--Katona function, Conway sequence, Takagi curve, and Pascal adic
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXII, Tome 411 (2013), pp. 135-147

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We study interrelations between the Kruskal–Katona function, Conway sequence, Takagi curve, and Pascal adic. Using the results of the current paper and, in particular, the convergence of the sequence $2a(n)-n$, where $a(n)$ is the Conway sequence, to the family of generalized Takagi curves, we prove a similar result for the Kruskal–Katona function. Moreover, a recursive method of computing the values of the Kruskal–Katona function is suggested. 
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     author = {A. R. Minabutdinov and I. E. Manaev},
     title = {The {Kruskal--Katona} function, {Conway} sequence, {Takagi} curve, and {Pascal} adic},
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A. R. Minabutdinov; I. E. Manaev. The Kruskal--Katona function, Conway sequence, Takagi curve, and Pascal adic. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXII, Tome 411 (2013), pp. 135-147. http://geodesic.mathdoc.fr/item/ZNSL_2013_411_a8/