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

Terms

a(0) =1a(1) =4a(2) =16a(3) =66a(4) =280a(5) =1216a(6) =5380a(7) =24144a(8) =109504a(9) =500488a(10) =2300128a(11) =10612224a(12) =49096720a(13) =227578432a(14) =1056304384a(15) =4907373600a(16) =22813275520a(17) =106100835328a(18) =493609021504