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

Terms

a(0) =1a(1) =2a(2) =5a(3) =17a(4) =61a(5) =221a(6) =812a(7) =3021a(8) =11344a(9) =42899a(10) =163146a(11) =623320a(12) =2390653a(13) =9198879a(14) =35494701a(15) =137290466a(16) =532149805a(17) =2066501909a(18) =8038146035a(19) =31312535610a(20) =122140123201a(21) =477002869614