Erroneous version of A002572.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =3a(5) =5a(6) =9a(7) =16a(8) =28a(9) =50a(10) =89a(11) =159a(12) =285a(13) =510a(14) =914a(15) =1639a(16) =2938a(17) =5269a(18) =9451a(19) =16952