a(n+1)=a(n)+a(n-1) if a(n-1) odd, a(n+1)=a(n)+a(n-1)/2 if a(n-1) even.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =4a(5) =7a(6) =9a(7) =16a(8) =25a(9) =33a(10) =58a(11) =91a(12) =120a(13) =211a(14) =271a(15) =482a(16) =753a(17) =994a(18) =1747a(19) =2244a(20) =3991a(21) =5113a(22) =9104a(23) =14217a(24) =18769a(25) =32986a(26) =51755a(27) =68248a(28) =120003a(29) =154127