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A259553
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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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%I #6 Jul 09 2015 20:35:17
%S 2,6,53,12034
%N 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}.
%C 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.
%e 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).
%Y Cf. A062714, A259482.
%K nonn,more
%O 1,1
%A _Jeffrey Shallit_, Jun 30 2015
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