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Can you help me please with the following question: There's a cubic symmetric m-dimensional grid. How many paths of N cells can be constructed inside this grid? The paths are without intersections, and not leaving the grid. Another condition is that each path necessary has to start at the most exterior layer. Another question is: how many path of length N of adjoint cells, starting at some specific point, can be constructed in this grid mesh cube? The possible movements ( if it's a 2D cube) are up-down-left-right. Similarly, in an arbitrary (finite) m dimension. Thanks

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