a(n) = ceiling((1 + sum of preceding terms) / 2) starting with a(0) = 1.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =4a(5) =6a(6) =9a(7) =14a(8) =21a(9) =31a(10) =47a(11) =70a(12) =105a(13) =158a(14) =237a(15) =355a(16) =533a(17) =799a(18) =1199a(19) =1798a(20) =2697a(21) =4046a(22) =6069a(23) =9103a(24) =13655a(25) =20482a(26) =30723a(27) =46085a(28) =69127a(29) =103691