Number of 4-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.

Terms

a(0) =16a(1) =208a(2) =976a(3) =2576a(4) =5056a(5) =8320a(6) =12368a(7) =17200a(8) =22816a(9) =29216a(10) =36400a(11) =44368a(12) =53120a(13) =62656a(14) =72976a(15) =84080a(16) =95968a(17) =108640a(18) =122096a(19) =136336a(20) =151360a(21) =167168a(22) =183760a(23) =201136a(24) =219296a(25) =238240a(26) =257968a(27) =278480a(28) =299776a(29) =321856