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A000434 Number of permutations of [n] in which the longest increasing run has length 4.
(Formerly M4556 N1938)
6
0, 0, 0, 1, 8, 67, 602, 5811, 60875, 690729, 8457285, 111323149, 1569068565, 23592426102, 377105857043, 6387313185576, 114303481217657, 2155348564847332, 42719058006864690, 887953677898186108, 19316200230609433690, 438920223893512987430 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

REFERENCES

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 261. (Values for n>=16 are incorrect.)

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Max Alekseyev, Table of n, a(n) for n = 1..100

Max A. Alekseyev, On the number of permutations with bounded runs length, arXiv preprint arXiv:1205.4581, 2012. - From N. J. A. Sloane, Oct 23 2012

EXAMPLE

a(5)=8 because we have (1235)4, (1245)3, (1345)2, (2345)1, 5(1234), 4(1235), 3(1245) and 2(1345), where the parentheses surround increasing runs of length 4.

CROSSREFS

Column 4 of A008304. Other columns: A000303, A000402, A000456, A000467.

Cf. A001250, A001251, A001252, A001253, A010026, A211318.

Sequence in context: A091645 A015574 A152055 * A250258 A192091 A050841

Adjacent sequences:  A000431 A000432 A000433 * A000435 A000436 A000437

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Better description from Emeric Deutsch, May 08 2004

Terms a(16)-a(18) corrected and further terms added by Max Alekseyev, May 20 2012

STATUS

approved

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Last modified August 17 13:03 EDT 2017. Contains 290635 sequences.