Essentially same as A004148.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =4a(6) =8a(7) =17a(8) =37a(9) =82a(10) =185a(11) =423a(12) =978a(13) =2283a(14) =5373a(15) =12735a(16) =30372a(17) =72832a(18) =175502