a(n) = 2*a(n-1) - a(n-3) + a(ceiling(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) =9a(6) =18a(7) =36a(8) =67a(9) =125a(10) =223a(11) =397a(12) =687a(13) =1187a(14) =2013a(15) =3406a(16) =5692a(17) =9496a(18) =15711a(19) =25953a(20) =42633a(21) =69952a(22) =114348a(23) =186750a(24) =304235a(25) =495309a(26) =805055a(27) =1307888a(28) =2122480a(29) =3443311