a(n) = 2*a(n-1) - a(n-3) + a(floor(n/2)), where a(0) = 1, a(1) = 1, a(2) = 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =8a(6) =16a(7) =30a(8) =56a(9) =100a(10) =178a(11) =308a(12) =532a(13) =902a(14) =1526a(15) =2550a(16) =4254a(17) =7038a(18) =11626a(19) =19098a(20) =31336a(21) =51224a(22) =83658a(23) =136288a(24) =221884a(25) =360642a(26) =585898a(27) =950814a(28) =1542512a(29) =2500652