Partially directed animals on the square lattice.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =19a(5) =62a(6) =206a(7) =694a(8) =2362a(9) =8101a(10) =27951a(11) =96905a(12) =337298a(13) =1177935a(14) =4125287a(15) =14482481a(16) =50950871a(17) =179584544a(18) =634020055a(19) =2241695805a(20) =7936423123a(21) =28131425351