Number of weakly alternating patterns of length n.

Terms

a(0) =1a(1) =1a(2) =3a(3) =11a(4) =43a(5) =203a(6) =1123a(7) =7235a(8) =53171a(9) =439595a(10) =4037371a(11) =40787579a(12) =449500595a(13) =5366500163a(14) =68997666867a(15) =950475759899