a(n) = a(n-1) + a(round(2*(n-1)/3)) + a(round((n-1)/3)) with a(1)=1, a(2)=2.

Terms

a(0) =1a(1) =2a(2) =4a(3) =7a(4) =12a(5) =18a(6) =27a(7) =41a(8) =57a(9) =79a(10) =110a(11) =144a(12) =192a(13) =256a(14) =325a(15) =416a(16) =538a(17) =666a(18) =828a(19) =1038a(20) =1257a(21) =1540a(22) =1892a(23) =2258a(24) =2715a(25) =3294a(26) =3889a(27) =4612a(28) =5497a(29) =6404