a(n) is the number of Fibonacci meanders of length m*n and central angle 360/m degrees where m = 2.

Terms

a(0) =1a(1) =3a(2) =6a(3) =13a(4) =30a(5) =70a(6) =167a(7) =405a(8) =992a(9) =2450a(10) =6090a(11) =15214a(12) =38165a(13) =96069a(14) =242530a(15) =613811a(16) =1556856a(17) =3956316a(18) =10070871a(19) =25674210a(20) =65541142a(21) =167517654a(22) =428635032a(23) =1097874434a(24) =2814611701a(25) =7221917871a(26) =18544968768a(27) =47655572191a(28) =122544150258a(29) =315313433594