A355089 Number of parity-alternating permutations of [n] avoiding the pattern 123.

1, 1, 1, 1, 3, 3, 10, 11, 37, 44, 146, 185, 603, 808, 2576, 3635, 11294, 16736, 50545, 78466, 230012, 373203, 1061236, 1795611, 4953447, 8721086, 23350320, 42691298, 111013825, 210379132, 531720722

Offset

0,5

Comments

A permutation is parity-alternating if it sends odd integers to odd integers, and even integers to even integers. It avoids 123 if there is no subsequence a..b..c with a < b < c. The values are computed by Michael Albert, see MathOverflow link.

The odd-indexed entries agree with the odd-indexed entries in A354208. A bijection is given by reversing the permutation.

Links

Table of n, a(n) for n=0..30.

Per Alexandersson, Samuel Asefa Fufa, Frether Getachew and Dun Qiu, Pattern-avoidance and Fuss-Catalan numbers, arXiv:2201.08168 [math.CO], 2022. See also J. Int. Seq. (2023) Vol. 26, Art. 23.4.2.

MathOverflow, 321-avoiding and parity-alternating permutations, Jun 06 2022.

Example

For n=4, the three permutations are 3412, 3214, 1432.
For n=5, we have 54321, 52143, 32541.
For n=6, we have 563412, 563214, 543612, 543216, 561432, 541632, 365412, 365214, 321654, 165432.

Crossrefs

Cf. A000108 (123-avoiding permutations), A010551 (parity-alternating permutations), A354208 (parity-alternating 321-avoiding permutations).

Sequence in context: A128015 A233256 A332955 * A218953 A081809 A359894

Adjacent sequences: A355086 A355087 A355088 * A355090 A355091 A355092

Keyword

nonn

Author

Per W. Alexandersson, Jun 18 2022

Status

approved