A jumping problem.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =7a(5) =13a(6) =17a(7) =30a(8) =60a(9) =107a(10) =197a(11) =257a(12) =454a(13) =908a(14) =1619a(15) =2981a(16) =3889a(17) =6870a(18) =13740a(19) =24499a(20) =45109a(21) =58849a(22) =103958a(23) =207916a(24) =370723a(25) =682597a(26) =890513a(27) =1573110a(28) =3146220a(29) =5609843