A062714 -id:A062714 - cp's OEIS frontend

A259553 Number of distinct (n!)-tuples, with integer entries between 0 and n, inclusive, where entries measure the length of the longest prefix of each of the n! permutations of 123...n that is a subsequence of some string over the alphabet {1,2,3,...n}.

2, 6, 53, 12034

Offset: 1

Jeffrey Shallit, Jun 30 2015

This sequence is an upper bound on A259482. (It is only an upper bound because two such n-tuples might be "equivalent" in the sense of the Myhill-Nerode theorem.) The length of the shortest string corresponding to (n,n,...,n) is given by A062714.

			For n = 2, where the permutations are 12 and 21, the six possible 2-tuples are (0,0) (corresponding to the empty string); (1,0) (corresponding to 1); (0,1) (corresponding to 2); (2,1) (corresponding to 12); (1,2) (corresponding to 21); (2,2) (corresponding to 121).

Cf. A062714, A259482.

A374086 Number of integer sequences on a circle of length A373728(n) containing all permutations of the set {1, 2, ..., n} as subsequences.

Original entry on oeis.org

1, 2, 18, 288, 14760

Offset: 1

Chai Wah Wu, Jun 27 2024

a(n) is a multiple of n!.

			a(1) = 1  as '1' is the only sequence of length A373728(1) = 1.
a(2) = 2  corresponding to the sequences of length A373728(2) = 2 : {'12', '21'}.
a(3) = 18 corresponding to the sequences of length A062714(3) = 4 : {'1213', '1231', '1232', '1312', '1321', '1323', '2123', '2131', '2132', '2312', '2313', '2321', '3121', '3123', '3132', '3212', '3213', '3231'}.

Cf. A062714, A373728, A374085.

cp's OEIS Frontend

A259553 Number of distinct (n!)-tuples, with integer entries between 0 and n, inclusive, where entries measure the length of the longest prefix of each of the n! permutations of 123...n that is a subsequence of some string over the alphabet {1,2,3,...n}.

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