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

Terms

a(0) =1a(1) =2a(2) =5a(3) =12a(4) =26a(5) =57a(6) =119a(7) =250a(8) =512a(9) =1050a(10) =2126a(11) =4309a(12) =8675a(13) =17469a(14) =35057a(15) =70364a(16) =140978a(17) =282468a(18) =565448a(19) =1131946a(20) =2264942a(21) =4532010a(22) =9066146a(23) =18136601a(24) =36277511a(25) =72563697a(26) =145136069a(27) =290289607a(28) =580596683a(29) =1161228423