a(n) is the sum of first n terms of A001285 (Thue-Morse sequence).

Terms

a(0) =0a(1) =1a(2) =3a(3) =5a(4) =6a(5) =8a(6) =9a(7) =10a(8) =12a(9) =14a(10) =15a(11) =16a(12) =18a(13) =19a(14) =21a(15) =23a(16) =24a(17) =26a(18) =27a(19) =28a(20) =30a(21) =31a(22) =33a(23) =35a(24) =36a(25) =37a(26) =39a(27) =41a(28) =42a(29) =44