a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2), starting 2,1.

Terms

a(0) =2a(1) =1a(2) =2a(3) =3a(4) =4a(5) =6a(6) =8a(7) =11a(8) =15a(9) =21a(10) =29a(11) =40a(12) =55a(13) =75a(14) =103a(15) =141a(16) =193a(17) =264a(18) =361a(19) =493a(20) =674a(21) =921a(22) =1258a(23) =1719a(24) =2348a(25) =3208a(26) =4382a(27) =5986a(28) =8177a(29) =11170