Number of symmetrically unique Dyck paths of semilength n and height three.

Terms

a(0) =1a(1) =3a(2) =11a(3) =31a(4) =91a(5) =250a(6) =690a(7) =1863a(8) =5017a(9) =13389a(10) =35621a(11) =94354a(12) =249352a(13) =657421a(14) =1730685a(15) =4550031a(16) =11950963a(17) =31365810a(18) =82274126a(19) =215711947a(20) =565376593a(21) =1481448697a(22) =3881041065a(23) =10165822434a(24) =26624745964a(25) =69725071281a(26) =182583838181a(27) =478093234315