Objects Counted By Central Delannoy Numbers

This work deals with Central Delannoy numbers, enumerated as Dn;n = (Dn)n_0rn= 1, 3, 13, 63, 321, 1683, 8989, 48639, . . ., which counts the number of latticernpaths running from (0; 0) to (n; n) by using the steps (1; 0), (0; 1) and (1; 1). Wernwill see some collection of examples that these numbers count. Also we will try tornsolve a problem on the Delannoy numbers, that is, proving that the central Delannoyrnnumbers also exist on the diagonal, in the rectangular format of another array ofrnnumbers, namely Sulanke numbe".

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