A309504 Number of cyclic permutations of length n avoiding the pattern 123.

1, 1, 1, 2, 4, 10, 24, 68, 188, 586, 1722, 5492, 16924, 55582, 177278, 594460, 1944980, 6628384, 22132112, 76421498, 259359036, 905416294, 3114033930, 10971347070, 38157201530

Offset

0,4

Links

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

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

Andrew Howroyd, PARI Program, Nov 2024.

Example

For n=3, there are two such permutations, 231 and 312.
The a(4) = 4 permutations are: 2413, 3142, 3421, 4312.
The a(5) = 10 permutations are: 25413, 35214, 35421, 41532, 43152, 43521, 45231, 53412, 54132, 54213.

Prog

(PARI) \\ See Links for program code.
for(n=0, 16, print1(E123(n), ", ")) \\ Andrew Howroyd, Nov 20 2024

Crossrefs

Cf. A000108 (number of permutations avoiding 123).

Cf. A309505, A309506, A309508.

Sequence in context: A003104 A121186 A309505 * A148088 A028506 A029893

Adjacent sequences: A309501 A309502 A309503 * A309505 A309506 A309507

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