Number of compositions of n whose run-lengths are not weakly increasing.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =1a(5) =4a(6) =8a(7) =24a(8) =55a(9) =128a(10) =282a(11) =625a(12) =1336a(13) =2855a(14) =6000a(15) =12551a(16) =26022a(17) =53744a(18) =110361a(19) =225914a(20) =460756a(21) =937413a(22) =1902370a(23) =3853445a(24) =7791647a(25) =15732468a(26) =31725191a(27) =63907437a(28) =128613224a(29) =258626480