Number of asymmetric rooted 2,3 cacti (triangular cacti with bridges).

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =6a(5) =16a(6) =42a(7) =115a(8) =319a(9) =909a(10) =2614a(11) =7622a(12) =22422a(13) =66556a(14) =198946a(15) =598617a(16) =1811205a(17) =5508015a(18) =16825307a(19) =51605568a(20) =158860950a(21) =490666293a(22) =1520106655a(23) =4722502437a(24) =14708971581a(25) =45921804883a(26) =143682973435a(27) =450477673623