a(n) = 2*a(n-1) + a(floor(n/2)), with a(1) = 1, a(2) = 2, a(3) = 4.

Terms

a(0) =1a(1) =2a(2) =4a(3) =10a(4) =22a(5) =48a(6) =100a(7) =210a(8) =430a(9) =882a(10) =1786a(11) =3620a(12) =7288a(13) =14676a(14) =29452a(15) =59114a(16) =118438a(17) =237306a(18) =475042a(19) =950966a(20) =1902814a(21) =3807414a(22) =7616614a(23) =15236848a(24) =30477316a(25) =60961920a(26) =121931128a(27) =243876932a(28) =487768540a(29) =975566532