Number of closed knight's tour diagrams of a 3 X n chessboard that have "Bergholtian symmetry".

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =4a(7) =0a(8) =0a(9) =0a(10) =8a(11) =0a(12) =48a(13) =0a(14) =152a(15) =0a(16) =352a(17) =0a(18) =1200a(19) =0a(20) =3752a(21) =0a(22) =12912a(23) =0a(24) =34768a(25) =0a(26) =122120a(27) =0a(28) =346128a(29) =0