Even sequences with period 2n.

Terms

a(0) =1a(1) =1a(2) =3a(3) =4a(4) =12a(5) =22a(6) =71a(7) =181a(8) =618a(9) =1957a(10) =6966a(11) =24367a(12) =89010a(13) =324766a(14) =1204815a(15) =4482400a(16) =16802826a(17) =63195016a(18) =238711285a(19) =904338163a(20) =3436380192a(21) =13089961012a(22) =49979421837a(23) =191221556269a(24) =733014218506