Number of binary strings of length 2n which contain the reversals of each of their two halves.

Terms

a(0) =4a(1) =12a(2) =42a(3) =106a(4) =300a(5) =654a(6) =1664a(7) =3300a(8) =7940a(9) =15018a(10) =34948a(11) =64396a(12) =147130a(13) =267404a(14) =604722a(15) =1090998a(16) =2453492a(17) =4409000a(18) =9886266a(19) =17729222a(20) =39693612a(21) =71108358a(22) =159076784a(23) =284820632a(24) =636918540a(25) =1140064414a(26) =2548902598a(27) =4561828606a(28) =10198077780a(29) =18250461694