a(n) = 2 + floor((1 + Sum_{j=1..n-1} a(j))/4).

Terms

a(0) =2a(1) =2a(2) =3a(3) =4a(4) =5a(5) =6a(6) =7a(7) =9a(8) =11a(9) =14a(10) =18a(11) =22a(12) =28a(13) =35a(14) =43a(15) =54a(16) =68a(17) =85a(18) =106a(19) =132a(20) =165a(21) =207a(22) =258a(23) =323a(24) =404a(25) =505a(26) =631a(27) =789a(28) =986a(29) =1232