Scaled row sum zero vector recursion:s=3; v(n)={s^(n+1),s^(n+1)-Sum[s^i,{i,2,n}],s^n,...,-1}.

Terms

a(0) =1a(1) =1a(2) =-1a(3) =3a(4) =-2a(5) =-1a(6) =9a(7) =-5a(8) =-3a(9) =-1a(10) =27a(11) =-14a(12) =-9a(13) =-3a(14) =-1a(15) =81a(16) =-41a(17) =-27a(18) =-9a(19) =-3a(20) =-1a(21) =243a(22) =-122a(23) =-81a(24) =-27a(25) =-9a(26) =-3a(27) =-1a(28) =729a(29) =-365