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

Terms

a(0) =1a(1) =2a(2) =6a(3) =21a(4) =72a(5) =258a(6) =945a(7) =3504a(8) =13128a(9) =49565a(10) =188260a(11) =718560a(12) =2753721a(13) =10588860a(14) =40835160a(15) =157871241a(16) =611669250a(17) =2374441380a(18) =9233006541a(19) =35956933050a(20) =140220970200a(21) =547490880981