The number of 3-alternating permutations of [n].

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =11a(6) =40a(7) =99a(8) =589a(9) =3194a(10) =11259a(11) =92159a(12) =666160a(13) =3052323a(14) =31799041a(15) =287316122a(16) =1620265923a(17) =20497038755a(18) =222237912664