a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-3*k-1,n-3*k).

Terms

a(0) =1a(1) =1a(2) =3a(3) =11a(4) =39a(5) =141a(6) =519a(7) =1933a(8) =7263a(9) =27479a(10) =104543a(11) =399543a(12) =1532779a(13) =5899167a(14) =22766607a(15) =88073091a(16) =341425551a(17) =1326019653a(18) =5158412943a(19) =20096457549a(20) =78396460299a(21) =306190920837