Triangle T(n,m) by rows: The number of tatami tilings of a 2 X n grid with dimers and 2*m monomers.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =3a(5) =9a(6) =1a(7) =4a(8) =18a(9) =7a(10) =6a(11) =35a(12) =26a(13) =1a(14) =9a(15) =64a(16) =73a(17) =10a(18) =13a(19) =112a(20) =179a(21) =52a(22) =1a(23) =19a(24) =192a(25) =403a(26) =194a(27) =13a(28) =28a(29) =323