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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =3a(5) =3a(6) =10a(7) =11a(8) =37a(9) =44a(10) =146a(11) =185a(12) =603a(13) =808a(14) =2576a(15) =3635a(16) =11294a(17) =16736a(18) =50545a(19) =78466a(20) =230012a(21) =373203a(22) =1061236a(23) =1795611a(24) =4953447a(25) =8721086a(26) =23350320a(27) =42691298a(28) =111013825a(29) =210379132