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

Terms

a(0) =1a(1) =3a(2) =5a(3) =9a(4) =15a(5) =23a(6) =35a(7) =53a(8) =73a(9) =101a(10) =141a(11) =185a(12) =247a(13) =329a(14) =417a(15) =533a(16) =689a(17) =853a(18) =1061a(19) =1331a(20) =1613a(21) =1977a(22) =2429a(23) =2899a(24) =3485a(25) =4227a(26) =4989a(27) =5915a(28) =7049a(29) =8211