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

Terms

a(0) =0a(1) =1a(2) =2a(3) =3a(4) =3a(5) =0a(6) =-9a(7) =-27a(8) =-54a(9) =-81a(10) =-81a(11) =0a(12) =243a(13) =729a(14) =1458a(15) =2187a(16) =2187a(17) =0a(18) =-6561a(19) =-19683a(20) =-39366a(21) =-59049a(22) =-59049a(23) =0a(24) =177147a(25) =531441a(26) =1062882a(27) =1594323a(28) =1594323a(29) =0