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

Terms

a(0) =1a(1) =2a(2) =3a(3) =7a(4) =15a(5) =30a(6) =60a(7) =112a(8) =209a(9) =373a(10) =664a(11) =1149a(12) =1985a(13) =3366a(14) =5695a(15) =9517a(16) =15877a(17) =26268a(18) =43392a(19) =71280a(20) =116956a(21) =191184a(22) =312237a(23) =508667a(24) =828135a(25) =1346018a(26) =2186735a(27) =3548701a(28) =5757079a(29) =9333118