Number of tatami tilings of a 2 X n grid (with monomers allowed).

Terms

a(0) =1a(1) =2a(2) =6a(3) =13a(4) =29a(5) =68a(6) =156a(7) =357a(8) =821a(9) =1886a(10) =4330a(11) =9945a(12) =22841a(13) =52456a(14) =120472a(15) =276681a(16) =635433a(17) =1459354a(18) =3351598a(19) =7697381a(20) =17678037a(21) =40599916a(22) =93242996a(23) =214144685a(24) =491811165a(25) =1129508406a(26) =2594063186a(27) =5957604017a(28) =13682413681a(29) =31423445328