Geodesic
Chocolate numbers
Journal of integer sequences, Tome 19 (2016) no. 1
In this paper, we consider a game played on a rectangular $m \times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along existing grid lines, until just $mn$ individual squares remain. This paper enumerates the number of ways to break an $m \times n$ bar, which we call chocolate numbers, and introduces four new sequences related to chocolate numbers. Using various techniques, we prove interesting divisibility results regarding chocolate number sequences.
Classification : 11B99
Keywords: generating function, hypergeometric function, periodicity, p-adic order, recursion, Riccati equation 
@article{JIS_2016__19_1_a4,
     author = {Ji,  Caleb and Khovanova,  Tanya and Park,  Robin and Song,  Angela},
     title = {Chocolate numbers},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {1},
     zbl = {1364.11067},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_1_a4/}
}
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Ji,  Caleb; Khovanova,  Tanya; Park,  Robin; Song,  Angela. Chocolate numbers. Journal of integer sequences, Tome 19 (2016) no. 1. http://geodesic.mathdoc.fr/item/JIS_2016__19_1_a4/