Zack's sequence (the pattern is evident).

Terms

a(0) =0a(1) =1a(2) =1a(3) =2a(4) =0a(5) =2a(6) =2a(7) =4a(8) =0a(9) =3a(10) =3a(11) =6a(12) =0a(13) =4a(14) =4a(15) =8a(16) =0a(17) =5a(18) =5a(19) =10a(20) =0a(21) =6a(22) =6a(23) =12a(24) =0a(25) =7a(26) =7a(27) =14a(28) =0a(29) =8