A309508 Number of cyclic permutations of length n avoiding the pattern 321.

1, 1, 1, 2, 4, 10, 24, 66, 178, 512, 1486, 4446, 13468, 41648, 130178, 412670, 1321418, 4274970, 13948966, 45890440, 152061154, 507292698, 1702753462, 5748085332, 19506240462

Offset

0,4

Comments

Comment from F. Chapoton, Sep 14 2021: (Start)

The maps sending a permutation to its inverse or to its reverse-complement define two commuting involutions on these sets of permutations.

The next terms in the sequence could be 41648, 130178, though these are counting Dyck words such that an associated permutation is cyclic, related but not obviously equivalent combinatorial objects. (End)

Links

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

Miklos Bona and Michael Cory, Cyclic Permutations Avoiding Pairs of Patterns of Length Three, arXiv:1805.05196 [math.CO], 2018.

Example

For n=3, there are two such permutations, 231 and 312.
The a(4) = 4 permutations are: 2341, 2413, 3142, 4123.
The a(5) = 10 permutations are: 23451, 23514, 24153, 25134, 31452, 31524, 34512, 41253, 45123, 51234.

Prog

(PARI) \\ See PARI link in A309504 for program code.
for(n=0, 16, print1(E321(n), ", ")) \\ Andrew Howroyd, Nov 20 2024

Crossrefs

Cf. A000108 (number of permutations avoiding 321).

Cf. A000957, A309504, A309505, A309506.

Sequence in context: A000682 A001997 A239605 * A000084 A057734 A151516

Adjacent sequences: A309505 A309506 A309507 * A309509 A309510 A309511

Keyword

nonn,more

Author

Miklos Bona, Aug 05 2019

Extensions

a(0)=1 prepended and a(13)-a(24) from Andrew Howroyd, Nov 17 2024

Status

approved