a(n) = ceiling((Sum_{k=1..n-1} a(k)) / 2) for n >= 2 starting with a(1) = 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =4a(6) =6a(7) =9a(8) =14a(9) =21a(10) =31a(11) =47a(12) =70a(13) =105a(14) =158a(15) =237a(16) =355a(17) =533a(18) =799a(19) =1199a(20) =1798a(21) =2697a(22) =4046a(23) =6069a(24) =9103a(25) =13655a(26) =20482a(27) =30723a(28) =46085a(29) =69127