a(n) = a(n-1) + (if a(n-1) is odd a(n-2) else a(n-3)) with a(0) = 0, a(1) = 1.

Terms

a(0) =0a(1) =1a(2) =1a(3) =2a(4) =3a(5) =5a(6) =8a(7) =11a(8) =19a(9) =30a(10) =41a(11) =71a(12) =112a(13) =153a(14) =265a(15) =418a(16) =571a(17) =989a(18) =1560a(19) =2131a(20) =3691a(21) =5822a(22) =7953a(23) =13775a(24) =21728a(25) =29681a(26) =51409a(27) =81090a(28) =110771a(29) =191861