Number of weak compositions of n such that the set of adjacent differences is a subset of {-1,1}.

Terms

a(0) =1a(1) =4a(2) =5a(3) =9a(4) =13a(5) =20a(6) =30a(7) =45a(8) =66a(9) =102a(10) =152a(11) =229a(12) =344a(13) =518a(14) =780a(15) =1180a(16) =1775a(17) =2676a(18) =4037a(19) =6088a(20) =9182a(21) =13852a(22) =20891a(23) =31512a(24) =47536a(25) =71706a(26) =108166a(27) =163172a(28) =246140a(29) =371303