Geodesic
Algoritms for enumeration of single-transition serial sequences
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 4, pp. 361-373

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Sets of $n$-valued single-transition serial sequences consisting of two serial subsequences (an increasing one and a decreasing one) determined by constraints on the number of series and on their lengths and heights are considered. Enumeration problems for sets of finite sequences in which the difference in height between the neighboring series is not less than some given value are solved. Algorithms that assign smaller numbers to the lexicographically lower-order sequences and smaller numbers to the lexicographically higher-order sequences are obtained. 
@article{SJVM_2010_13_4_a0,
     author = {V. A. Amelkin},
     title = {Algoritms for enumeration of single-transition serial sequences},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {361--373},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a0/}
}
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V. A. Amelkin. Algoritms for enumeration of single-transition serial sequences. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 4, pp. 361-373. http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a0/