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 A354208 Number of parity-alternating permutations of [n] avoiding the pattern 321. 2
 1, 1, 1, 1, 2, 3, 6, 11, 22, 44, 89, 185, 382, 808, 1702, 3635, 7779, 16736, 36229, 78466, 171238, 373203, 819186, 1795611, 3958662, 8721086, 19294525, 42691298, 94733886, 210379132, 468084856, 1042703207, 2325575076, 5193931583, 11609749877, 25986720374, 58203955771 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000108 (321-avoiding permutations), A010551 (parity-alternating permutations). Sequence in context: A027214 A192652 A132831 * A007477 A274936 A244521 Adjacent sequences: A354205 A354206 A354207 * A354209 A354210 A354211 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

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Last modified June 5 16:06 EDT 2023. Contains 363137 sequences. (Running on oeis4.)