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

Author

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

Keywords

• nonn

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

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

Crossrefs

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

Programs

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]

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