Number of nonconsecutive chess tableaux with n cells.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =2a(6) =4a(7) =5a(8) =10a(9) =15a(10) =33a(11) =52a(12) =126a(13) =213a(14) =537a(15) =991a(16) =2563a(17) =5118a(18) =13670a(19) =29171a(20) =81069a(21) =180813a(22) =525755a(23) =1216996a(24) =3693934a(25) =8843831a(26) =27797975a(27) =69106326a(28) =223116931a(29) =577433770