Number of compositions of n with no adjacent triples (..., x, y, z, ...) where x <= y <= z.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =10a(6) =17a(7) =29a(8) =50a(9) =84a(10) =143a(11) =241a(12) =408a(13) =688a(14) =1162a(15) =1959a(16) =3305a(17) =5571a(18) =9393a(19) =15832a(20) =26688a(21) =44980a(22) =75812a(23) =127769a(24) =215338a(25) =362911a(26) =611620a(27) =1030758a(28) =1737131a(29) =2927556