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A000303 Number of permutations of [n] in which the longest increasing run has length 2.
(Formerly M3522 N1430)
6
0, 1, 4, 16, 69, 348, 2016, 13357, 99376, 822040, 7477161, 74207208, 797771520, 9236662345, 114579019468, 1516103040832, 21314681315997, 317288088082404, 4985505271920096, 82459612672301845, 1432064398910663704, 26054771465540507272 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 261, Table 7.4.1.

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(3)=4 because we have (13)2, 2(13), (23)1, 3(12), where the parentheses surround increasing runs of length 2.

CROSSREFS

Column 2 of A008304. Other columns: A000402, A000434, A000456, A000467, A230055.

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

Sequence in context: A228950 A231297 A231358 * A144316 A180145 A133789

Adjacent sequences:  A000300 A000301 A000302 * A000304 A000305 A000306

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Better description from Emeric Deutsch, May 08 2004

Edited and extended by Max Alekseyev, May 20 2012

STATUS

approved

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Last modified March 25 13:25 EDT 2017. Contains 284080 sequences.