A217057 Number of permutations in S_n containing exactly one increasing subsequence of length 4.

0, 0, 0, 0, 1, 12, 102, 770, 5545, 39220, 276144, 1948212, 13817680, 98679990, 710108396, 5150076076, 37641647410, 277202062666, 2056218941678, 15358296210724, 115469557503753, 873561194459596, 6647760790457218, 50871527629923754, 391345137795371013

Offset

0,6

Links

Brian Nakamura and Doron Zeilberger, Table of n, a(n) for n = 0..70

Andrew R. Conway and Anthony J. Guttmann, Counting occurrences of patterns in permutations, arXiv:2306.12682 [math.CO], 2023. See p. 16.

Brian Nakamura and Doron Zeilberger, Using Noonan-Zeilberger Functional Equations to enumerate (in Polynomial Time!) Generalized Wilf classes; Local copy, pdf file only, no active links

Brian Nakamura and Doron Zeilberger, Using Noonan-Zeilberger Functional Equations to enumerate (in Polynomial Time!) Generalized Wilf classes, arXiv preprint arXiv:1209.2353, 2012.

Wikipedia, Enumerations of specific permutation classes

Wikipedia, Subsequence

Example

a(4) = 1: 1234.
a(5) = 12: 12453, 12534, 13425, 13452, 14235, 15234, 23145, 23415, 23451, 31245, 41235, 51234.

Maple

# programs can be obtained from the Nakamura & Zeilberger link.

Crossrefs

Cf. A005802, A117158, A158005, A214015, A214152.

Sequence in context: A261483 A082151 A125375 * A356836 A240462 A126533

Adjacent sequences: A217054 A217055 A217056 * A217058 A217059 A217060

Keyword

nonn

Author

Alois P. Heinz, Sep 25 2012

Status

approved