Number of sequences with terms 1, 2 or 3 summing to n with no three consecutive 1's.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =10a(6) =17a(7) =30a(8) =52a(9) =90a(10) =156a(11) =271a(12) =470a(13) =815a(14) =1414a(15) =2453a(16) =4255a(17) =7381a(18) =12804a(19) =22211a(20) =38529a(21) =66836a(22) =115940a(23) =201120a(24) =348881a(25) =605201a(26) =1049837a(27) =1821143a(28) =3159121a(29) =5480100