Number of compositions of n whose run-lengths are neither weakly increasing nor weakly decreasing.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =3a(7) =8a(8) =27a(9) =75a(10) =185a(11) =441a(12) =1025a(13) =2276a(14) =4985a(15) =10753a(16) =22863a(17) =48142a(18) =100583a(19) =208663a(20) =430563a(21) =884407a(22) =1809546a(23) =3690632a(24) =7506774a(25) =15233198a(26) =30851271a(27) =62377004a(28) =125934437a(29) =253936064