a(n) = Sum_{k=0..floor(2*n/3)} binomial(4*n-4*k,2*k).

Terms

a(0) =1a(1) =1a(2) =7a(3) =30a(4) =137a(5) =644a(6) =2936a(7) =13625a(8) =62701a(9) =289547a(10) =1335378a(11) =6161329a(12) =28424456a(13) =131135696a(14) =604991601a(15) =2791106585a(16) =12876698159a(17) =59406240678a(18) =274068969337