Sequence showing kinds of "waves", built as follows in comments.

Terms

a(0) =1a(1) =6a(2) =26a(3) =2a(4) =100a(5) =2a(6) =4a(7) =2a(8) =396a(9) =2a(10) =4a(11) =2a(12) =12a(13) =2a(14) =4a(15) =2a(16) =1580a(17) =2a(18) =4a(19) =2a(20) =12a(21) =2a(22) =4a(23) =2a(24) =44a(25) =2a(26) =4a(27) =2a(28) =12a(29) =2