Let u(1)=u(2)=u(3)=1, u(n)=sign(u(n-1)-u(n-2))/(u(n-3)+1); then a(n) is the numerator of u(n).

Terms

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