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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =5a(5) =9a(6) =15a(7) =27a(8) =45a(9) =77a(10) =127a(11) =213a(12) =349a(13) =577a(14) =941a(15) =1545a(16) =2513a(17) =4103a(18) =6661a(19) =10841a(20) =17579a(21) =28547a(22) =46253a(23) =75013a(24) =121479a(25) =196841a(26) =318669a(27) =516087a(28) =835333a(29) =1352361