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

Terms

a(0) =1a(1) =1a(2) =1a(3) =5a(4) =19a(5) =49a(6) =137a(7) =481a(8) =1645a(9) =5259a(10) =17309a(11) =59477a(12) =203931a(13) =693865a(14) =2384149a(15) =8277773a(16) =28797631a(17) =100312525a(18) =350891175a(19) =1232122535a(20) =4335809699a(21) =15287669469a(22) =54029225569a(23) =191351513905a(24) =678850904981