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

Terms

a(0) =1a(1) =0a(2) =1a(3) =4a(4) =7a(5) =12a(6) =30a(7) =68a(8) =137a(9) =292a(10) =644a(11) =1380a(12) =2936a(13) =6324a(14) =13625a(15) =29216a(16) =62701a(17) =134784a(18) =289547a(19) =621708a(20) =1335378a(21) =2868620a(22) =6161329a(23) =13233352a(24) =28424456a(25) =61053608a(26) =131135696a(27) =281665480a(28) =604991601a(29) =1299461088