A355089 - OEIS

%I #12 May 04 2023 09:52:28

%S 1,1,1,1,3,3,10,11,37,44,146,185,603,808,2576,3635,11294,16736,50545,

%T 78466,230012,373203,1061236,1795611,4953447,8721086,23350320,

%U 42691298,111013825,210379132,531720722

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

%C 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.

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

%H Per Alexandersson, Samuel Asefa Fufa, Frether Getachew and Dun Qiu, <a href="https://arxiv.org/abs/2201.08168">Pattern-avoidance and Fuss-Catalan numbers</a>, arXiv:2201.08168 [math.CO], 2022. See also <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Getachew/get3.html">J. Int. Seq.</a> (2023) Vol. 26, Art. 23.4.2.

%H MathOverflow, <a href="https://mathoverflow.net/questions/424040/321-avoiding-and-parity-alternating-permutations">321-avoiding and parity-alternating permutations</a>, Jun 06 2022.

%e For n=4, the three permutations are 3412, 3214, 1432.

%e For n=5, we have 54321, 52143, 32541.

%e For n=6, we have 563412, 563214, 543612, 543216, 561432, 541632, 365412, 365214, 321654, 165432.

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

%K nonn

%O 0,5

%A _Per W. Alexandersson_, Jun 18 2022