a(n)=a(n-1)+floor((a(n-2)+a(n-3))/2), with a(n)=n for n<3.

Terms

a(0) =0a(1) =1a(2) =2a(3) =2a(4) =3a(5) =5a(6) =7a(7) =11a(8) =17a(9) =26a(10) =40a(11) =61a(12) =94a(13) =144a(14) =221a(15) =340a(16) =522a(17) =802a(18) =1233a(19) =1895a(20) =2912a(21) =4476a(22) =6879a(23) =10573a(24) =16250a(25) =24976a(26) =38387a(27) =59000a(28) =90681a(29) =139374