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As a model for continuous curves in digital geometry, we study the Khalimsky-continuous functions defined on the integers and with values in the set of integers or the set of natural numbers. We determine the number of such functions on a given interval. It turns out that these numbers are related to the Delannoy and Schröder arrays, and a relation between these numbers is established.
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Shiva Samieinia, The number of continuous curves in digital geometry. Port. Math. 67 (2010), no. 1, pp. 75–89DOI 10.4171/PM/1858