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

Terms

a(0) =1a(1) =0a(2) =2a(3) =1a(4) =6a(5) =7a(6) =21a(7) =34a(8) =80a(9) =149a(10) =319a(11) =629a(12) =1299a(13) =2617a(14) =5336a(15) =10828a(16) =21992a(17) =44713a(18) =90741a(19) =184524a(20) =374521a(21) =761403a(22) =1545839a(23) =3141826a(24) =6380241a(25) =12964858a(26) =26332515a(27) =53501860a(28) =108676262a(29) =220790480