Number of alternating patterns of length n.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =22a(5) =102a(6) =562a(7) =3618a(8) =26586a(9) =219798a(10) =2018686a(11) =20393790a(12) =224750298a(13) =2683250082a(14) =34498833434a(15) =475237879950