Number of parity-alternating permutations of [n] avoiding the pattern 321.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =3a(6) =6a(7) =11a(8) =22a(9) =44a(10) =89a(11) =185a(12) =382a(13) =808a(14) =1702a(15) =3635a(16) =7779a(17) =16736a(18) =36229a(19) =78466a(20) =171238a(21) =373203a(22) =819186a(23) =1795611a(24) =3958662a(25) =8721086a(26) =19294525a(27) =42691298a(28) =94733886a(29) =210379132