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

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =9a(5) =13a(6) =19a(7) =29a(8) =41a(9) =57a(10) =79a(11) =103a(12) =137a(13) =183a(14) =233a(15) =299a(16) =387a(17) =479a(18) =595a(19) =745a(20) =901a(21) =1103a(22) =1355a(23) =1617a(24) =1945a(25) =2361a(26) =2789a(27) =3309a(28) =3945a(29) =4597