a(n) = Sum_{j=0..floor(n/3)} (-1)^j*binomial(n,3*j).

Terms

a(0) =1a(1) =1a(2) =1a(3) =0a(4) =-3a(5) =-9a(6) =-18a(7) =-27a(8) =-27a(9) =0a(10) =81a(11) =243a(12) =486a(13) =729a(14) =729a(15) =0a(16) =-2187a(17) =-6561a(18) =-13122a(19) =-19683a(20) =-19683a(21) =0a(22) =59049a(23) =177147a(24) =354294a(25) =531441a(26) =531441a(27) =0a(28) =-1594323a(29) =-4782969