T(n,k) = Number of n-turn rook's tours on a k X k board summed over all starting positions.

Terms

a(0) =1a(1) =4a(2) =0a(3) =9a(4) =8a(5) =0a(6) =16a(7) =36a(8) =8a(9) =0a(10) =25a(11) =96a(12) =108a(13) =8a(14) =0a(15) =36a(16) =200a(17) =480a(18) =288a(19) =0a(20) =0a(21) =49a(22) =360a(23) =1400a(24) =2208a(25) =720a(26) =0a(27) =0a(28) =64a(29) =588