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

Terms

a(0) =1a(1) =2a(2) =3a(3) =10a(4) =18a(5) =40a(6) =79a(7) =140a(8) =262a(9) =491a(10) =842a(11) =1483a(12) =2605a(13) =4368a(14) =7482a(15) =12732a(16) =21096a(17) =35351a(18) =59131a(19) =97166a(20) =160744a(21) =265532a(22) =433898a(23) =712302a(24) =1167558a(25) =1901218a(26) =3104389a(27) =5065229a(28) =8229240a(29) =13392126