a(n) = 4 + floor((3 + Sum_{j=1..n-1} a(j))/4).

Terms

a(0) =4a(1) =5a(2) =7a(3) =8a(4) =10a(5) =13a(6) =16a(7) =20a(8) =25a(9) =31a(10) =39a(11) =49a(12) =61a(13) =76a(14) =95a(15) =119a(16) =149a(17) =186a(18) =233a(19) =291a(20) =364a(21) =455a(22) =568a(23) =710a(24) =888a(25) =1110a(26) =1387a(27) =1734a(28) =2168a(29) =2710