Considering a so-called square k-zig-zag shape as a part of the regular square grid as ak-zig-zag digraph, we give values to its vertices according to the number of the shortest pathsfrom a base vertex. It provides several integer sequences, whose higher-order homogeneousrecurrences are determined by the help of a special matrix recurrence. We also define aspecial zig-zag shape based on the spatial cube grid, and we give recurrence relation for oneof their digraph walk.
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