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 321 if there is no subsequence a..b..c with a > b > c. The values are computed by Michael Albert, see MathOverflow link.
LINKS
Peter J. Taylor, Table of n, a(n) for n = 0..50
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.
Nathan Williams, Oberwolfach Problem Session: Enumerative Combinatorics 2022, Univ. Texas Dallas (2023). See example 3.4, where this sequence is misidentified by typographical error.
EXAMPLE
For n=4, the two permutations are 1234, 3412.
For n=5, we have 12345, 34125, 14523.
For n=6, we have 123456, 341256, 145236, 125634, 561234, 345612.
CROSSREFS
KEYWORD
nonn
AUTHOR
Per W. Alexandersson, Jun 06 2022
EXTENSIONS
Offset corrected and terms a(30) and beyond from Peter J. Taylor, Jun 10 2022
STATUS
approved