a(n) = a(n-1)+ceiling(a(n-2)/2) with a(0)=0, a(1)=1.

Terms

a(0) =0a(1) =1a(2) =1a(3) =2a(4) =3a(5) =4a(6) =6a(7) =8a(8) =11a(9) =15a(10) =21a(11) =29a(12) =40a(13) =55a(14) =75a(15) =103a(16) =141a(17) =193a(18) =264a(19) =361a(20) =493a(21) =674a(22) =921a(23) =1258a(24) =1719a(25) =2348a(26) =3208a(27) =4382a(28) =5986a(29) =8177