A177476 Number of partitions of order n avoiding the consecutive pattern 231'1.

1, 1, 2, 6, 20, 83, 402, 2245, 14192, 100650, 792508, 6859260, 64772648, 662630653, 7301841444, 86212535179, 1085834949064, 14530898302390, 205897508769218, 3079580500287978, 48485072137150344, 801518797091165406, 13881049047327393608, 251325130816997882224, 4748240560493406374592

Offset

0,3

Comments

To avoid 231'1 means not to have four consecutive letters such that if the third letter is removed, then in the obtained 3 letter word the smallest letter is the last one, and the largest letter is the second one.

Links

Table of n, a(n) for n=0..24.

S. Kitaev, Introduction to partially ordered patterns, Discrete Applied Mathematics 155 (2007), 929-944.

Mathematica

ok[{x_, y_, _, z_}] := Not[x>z && y>z && y>x]; a[n_] := Length@ Select[ Permutations@ Range@ n, AllTrue[ Partition[#, 4, 1], ok] &]; a /@ Range[0, 9]

Crossrefs

Cf. A117156, A177470, A177471, A177472, A177473, A177475, A177477, A177478, A177479, A177480, A177481, A177482, A177483, A177484, A376694.

Sequence in context: A260788 A337274 A115084 * A266600 A177474 A372987

Adjacent sequences: A177473 A177474 A177475 * A177477 A177478 A177479

Keyword

nonn

Author

Signy Olafsdottir (signy06(AT)ru.is), May 09 2010

Extensions

a(0), a(10)-a(14) from Alois P. Heinz, Mar 10 2020

a(15)-a(16) from Giovanni Resta, Mar 11 2020

a(17)-a(24) from Max Alekseyev, Oct 02 2024

Status

approved