Geodesic
Sequences by Number of w-Rises
Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 317-319

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An m-permutation of n, repetitions allowed, is an m-sequence (1) A w-rise is a pair (ei, ei+1) such that ei+1-ei≥w>0. In this note we find an expression for Tk, w(n, m), the number of m-sequences having precisely k w-rises. The case w = 1 is given in [1] [2]. Also, when w = 1 we give the number when each of the integers 1, 2, ..., r must appear at least once. 
Abramson, Morton. Sequences by Number of w-Rises. Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 317-319. doi: 10.4153/CMB-1975-059-6
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     title = {Sequences by {Number} of {w-Rises}},
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