A309506 Number of cyclic permutations of length n avoiding the pattern 231 (equivalently, 312).

1, 1, 1, 1, 2, 5, 12, 30, 86, 253, 748, 2274, 7152, 22890, 74189, 243342, 808599, 2716549, 9213420, 31498358, 108483093, 376145636, 1312463081, 4605569378, 16245866825

Offset

0,5

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.

Example

For n=4, there are two such permutations, 4123 and 4312.
The a(5) = 5 permutations are 51234, 51423, 53124, 54132, 54213.

Prog

(PARI) \\ See PARI link in A309504 for program code.
for(n=0, 16, print1(E231(n), ", ")) \\ Andrew Howroyd, Nov 20 2024

Crossrefs

Cf. A000108 (number of permutations avoiding 231).

Cf. A309504, A309505, A309508.

Sequence in context: A363912 A261788 A112412 * A319557 A261937 A305311

Adjacent sequences: A309503 A309504 A309505 * A309507 A309508 A309509

Keyword

nonn,more,changed

Author

Miklos Bona, Aug 05 2019

Extensions

a(1)=1 (confirmed by author) inserted by Alexander Burstein, Jul 20 2020

a(0)=1 prepended and a(13)-a(24) from Andrew Howroyd, Nov 20 2024

Status

approved