a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-6*k,n-3*k).

Terms

a(0) =1a(1) =2a(2) =6a(3) =19a(4) =68a(5) =246a(6) =905a(7) =3364a(8) =12624a(9) =47715a(10) =181392a(11) =692808a(12) =2656441a(13) =10219208a(14) =39423792a(15) =152461079a(16) =590861182a(17) =2294182428a(18) =8922674221a(19) =34754402618a(20) =135552346392a(21) =529335200219