a(n) = a(n-1) + a(n-2) + 2 a([n/2]), where a(0) = 1, a(1) = 2, a(2) = 3.

Terms

a(0) =1a(1) =2a(2) =3a(3) =9a(4) =18a(5) =33a(6) =69a(7) =120a(8) =225a(9) =381a(10) =672a(11) =1119a(12) =1929a(13) =3186a(14) =5355a(15) =8781a(16) =14586a(17) =23817a(18) =39165a(19) =63744a(20) =104253a(21) =169341a(22) =275832a(23) =447411a(24) =727101a(25) =1178370a(26) =1911843a(27) =3096585a(28) =5019138a(29) =8126433