a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-5*k,n-3*k).

Terms

a(0) =1a(1) =2a(2) =6a(3) =21a(4) =73a(5) =262a(6) =960a(7) =3562a(8) =13347a(9) =50393a(10) =191406a(11) =730555a(12) =2799622a(13) =10765092a(14) =41513751a(15) =160490906a(16) =621805286a(17) =2413738744a(18) =9385635299a(19) =36550685683a(20) =142534105563a(21) =556514122937