Number of compositions of n with parts in N which avoid the adjacent pattern 111.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =7a(5) =13a(6) =24a(7) =46a(8) =89a(9) =170a(10) =324a(11) =618a(12) =1183a(13) =2260a(14) =4318a(15) =8249a(16) =15765a(17) =30123a(18) =57556a(19) =109973a(20) =210137a(21) =401525a(22) =767216a(23) =1465963a(24) =2801115a(25) =5352275a(26) =10226930a(27) =19541236a(28) =37338699a(29) =71345449