A309505 Number of cyclic permutations of length n that avoid the pattern 132 (equivalently, 213).

1, 1, 1, 2, 4, 10, 24, 68, 182, 544, 1574, 4888, 14864, 47610, 149964, 491802, 1592198, 5318936, 17593170, 59679516, 200805614, 689988886, 2354489616, 8178944510, 28240716098

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.

Brice Huang, An Upper Bound on the Number of (132,213)-Avoiding Cyclic Permutations, arXiv:1808.08462 [math.CO], 2018-2019.

Example

For n=3, there are two such permutations, 231 and 312.
The a(4) = 4 permutations are: 2341, 3421, 4123, 4312.
The a(5) = 10 permutations are: 23451, 34251, 34512, 43521, 45123, 45231, 51234, 53124, 53412, 54213.

Prog

(PARI) \\ See PARI link in A309504 for program code.
for(n=1, 16, print1(E213(n), ", ")) \\ Andrew Howroyd, Nov 20 2024

Crossrefs

Cf. A000108 (number of permutations avoiding 132).

Cf. A309504, A309506, A309508.

Sequence in context: A151516 A003104 A121186 * A309504 A148088 A028506

Adjacent sequences: A309502 A309503 A309504 * A309506 A309507 A309508

Keyword

nonn,more,changed

Author

Miklos Bona, Aug 05 2019

Extensions

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

Status

approved