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

1,1

Comments

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.

Links

Table of n, a(n) for n=1..4.

Example

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).

Crossrefs

Cf. A062714, A259482.

Sequence in context: A277363 A156340 A337510 * A327425 A262046 A280982

Adjacent sequences: A259550 A259551 A259552 * A259554 A259555 A259556

Keyword

nonn,more

Author

Jeffrey Shallit, Jun 30 2015

Status

approved