a(n) = a(n-1) + a(n-2) + a([n/3]), where a(0) = 1, a(1) = 1, a(2) = 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =5a(5) =9a(6) =15a(7) =25a(8) =41a(9) =69a(10) =113a(11) =185a(12) =303a(13) =493a(14) =801a(15) =1303a(16) =2113a(17) =3425a(18) =5553a(19) =8993a(20) =14561a(21) =23579a(22) =38165a(23) =61769a(24) =99975a(25) =161785a(26) =261801a(27) =423655a(28) =685525a(29) =1109249