a(1) = 0, a(2) = 1; and for n > 2, a(n) = 2*a(A285712(n)) + [1 == (n mod 3)].

Terms

a(0) =0a(1) =1a(2) =2a(3) =5a(4) =2a(5) =10a(6) =21a(7) =4a(8) =42a(9) =85a(10) =10a(11) =170a(12) =5a(13) =4a(14) =340a(15) =681a(16) =20a(17) =8a(18) =1363a(19) =42a(20) =2726a(21) =5453a(22) =8a(23) =10906a(24) =11a(25) =84a(26) =21812a(27) =21a(28) =170a(29) =43624