Number of 3-turn rook's tours on an n X n board summed over all starting positions.

Terms

a(0) =0a(1) =8a(2) =108a(3) =480a(4) =1400a(5) =3240a(6) =6468a(7) =11648a(8) =19440a(9) =30600a(10) =45980a(11) =66528a(12) =93288a(13) =127400a(14) =170100a(15) =222720a(16) =286688a(17) =363528a(18) =454860a(19) =562400a(20) =687960a(21) =833448a(22) =1000868a(23) =1192320a(24) =1410000a(25) =1656200a(26) =1933308a(27) =2243808a(28) =2590280a(29) =2975400