Enumeration of Pairs of Sequences by Rises, Falls and Levels.
Manuscripta mathematica, Tome 19 (1976), pp. 211-244.

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@article{MM2_1976__19_154415,
     author = {L. Carlitz and R. Scoville},
     title = {Enumeration of {Pairs} of {Sequences} by {Rises,} {Falls} and {Levels.}},
     journal = {Manuscripta mathematica},
     pages = {211--244},
     publisher = {mathdoc},
     volume = {19},
     year = {1976},
     zbl = {0348.05006},
     url = {http://geodesic.mathdoc.fr/item/MM2_1976__19_154415/}
}
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L. Carlitz; R. Scoville. Enumeration of Pairs of Sequences by Rises, Falls and Levels.. Manuscripta mathematica, Tome 19 (1976), pp. 211-244. http://geodesic.mathdoc.fr/item/MM2_1976__19_154415/