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 A258683 Total number of permutations on {1,2,...,n} that have a unique longest increasing subsequence and a unique longest decreasing subsequence. 1
 1, 0, 0, 0, 2, 16, 120, 938, 8014, 74060, 748628, 8163156, 96429784 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS By definition, a(n) <= A167995(n). LINKS Table of n, a(n) for n=1..13. Manfred Scheucher, C Code EXAMPLE the two permutation of {1,2,...,5}: {2, 5, 3, 1, 4} {4, 1, 3, 5, 2} 8 of the 16 permutations of {1,2,...,6} (others reversed): {1, 3, 6, 4, 2, 5} {1, 5, 2, 4, 6, 3} {2, 3, 6, 4, 1, 5} {2, 5, 3, 1, 4, 6} {2, 6, 3, 1, 4, 5} {2, 6, 5, 3, 1, 4} {3, 6, 4, 2, 1, 5} {3, 6, 4, 2, 5, 1} PROG (Sage) def A258683(n): return len([p for p in permutations(n) if len(p.longest_increasing_subsequences())* len(p.reverse().longest_increasing_subsequences())==1]) # Manfred Scheucher, Jun 07 2015 CROSSREFS Cf. A167995, A167999, A168502. Sequence in context: A112710 A046105 A086854 * A026129 A026158 A025185 Adjacent sequences: A258680 A258681 A258682 * A258684 A258685 A258686 KEYWORD nonn,more AUTHOR Manfred Scheucher, Jun 07 2015 STATUS approved

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Last modified May 27 14:41 EDT 2024. Contains 372861 sequences. (Running on oeis4.)