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

Terms

a(0) =1a(1) =3a(2) =10a(3) =36a(4) =133a(5) =498a(6) =1882a(7) =7161a(8) =27391a(9) =105210a(10) =405499a(11) =1567332a(12) =6072724a(13) =23578221a(14) =91712089a(15) =357301827a(16) =1393986898a(17) =5445422340a(18) =21296030401a(19) =83370591273a(20) =326688422203