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

Terms

a(0) =0a(1) =0a(2) =1a(3) =2a(4) =0a(5) =5a(6) =10a(7) =2a(8) =21a(9) =42a(10) =4a(11) =85a(12) =0a(13) =0a(14) =171a(15) =342a(16) =10a(17) =5a(18) =684a(19) =20a(20) =1369a(21) =2738a(22) =4a(23) =5477a(24) =0a(25) =42a(26) =10955a(27) =8a(28) =84a(29) =21911