Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =16a(6) =29a(7) =56a(8) =101a(9) =181a(10) =327a(11) =583a(12) =1023a(13) =1820a(14) =3207a(15) =5631a(16) =9905a(17) =17394a(18) =30489a(19) =53481a(20) =93725a(21) =164169a(22) =287606a(23) =503672a(24) =881834a(25) =1544018a(26) =2703161a(27) =4731860a(28) =8283291a(29) =14499392