The number of 4-alternating permutations of [n].

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =4a(6) =19a(7) =78a(8) =217a(9) =496a(10) =3961a(11) =25442a(12) =105963a(13) =349504a(14) =3908059a(15) =34227438a(16) =190065457a(17) =819786496a(18) =11785687921a(19) =130746521282a(20) =907546301523