Number of non-unimodal compositions of n covering an initial interval of positive integers.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =1a(6) =5a(7) =14a(8) =35a(9) =83a(10) =193a(11) =417a(12) =890a(13) =1847a(14) =3809a(15) =7805a(16) =15833a(17) =32028a(18) =64513a(19) =129671a(20) =260155a(21) =521775a(22) =1044982a(23) =2092692a(24) =4188168a(25) =8381434a(26) =16767650a(27) =33544423a(28) =67098683a(29) =134213022