Triangular array: T(n,k) is the 2-row creation rook number to place k rooks on a 3 x n board.

Terms

a(0) =1a(1) =1a(2) =3a(3) =1a(4) =6a(5) =12a(6) =1a(7) =9a(8) =36a(9) =60a(10) =1a(11) =12a(12) =72a(13) =240a(14) =360a(15) =1a(16) =15a(17) =120a(18) =600a(19) =1800a(20) =2520a(21) =1a(22) =18a(23) =180a(24) =1200a(25) =5400a(26) =15120a(27) =20160a(28) =1a(29) =21