a(1)=1. For n >= 2, a(n) = 2*a(n-1) + (number of composites among first n-1 terms of the sequence).

Terms

a(0) =1a(1) =2a(2) =4a(3) =9a(4) =20a(5) =43a(6) =89a(7) =181a(8) =365a(9) =734a(10) =1473a(11) =2952a(12) =5911a(13) =11830a(14) =23669a(15) =47347a(16) =94704a(17) =189419a(18) =378850a(19) =757713a(20) =1515440a(21) =3030895a(22) =6061806a(23) =12123629a(24) =24247276a(25) =48494571a(26) =96989162a(27) =193978345a(28) =387956712a(29) =775913447