Leonard triples extended from a given totally almost bipartite Leonard pair of Bannai/Ito type

Let K denote a field of characteristic zero and let d denote an integer at least 3. LetA=(−1)d(02d+10102d202d−13.......d+3d−10d+20dd+1) andA⁎=diag((−1)d(2d+1),…,−7,5,−3,1) be two matrices in Matd+1(K). Then A,A⁎ is a totally almost bipartite Leonard pair on Kd+1 of Bannai/Ito type. In this paper, we determine all the matrices Aε∈Matd+1(K) such that A,A⁎,Aε form a Leonard triple on Kd+1.