An "eta-sequence": floor((n+1)*sqrt(2) + 1/2) - floor(n*sqrt(2) + 1/2).

Terms

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