a(n) = Sum[d|n, d==1 (mod 3), d^2] - Sum[d|n, d==2 (mod 3), d^2].

Terms

a(0) =1a(1) =-3a(2) =1a(3) =13a(4) =-24a(5) =-3a(6) =50a(7) =-51a(8) =1a(9) =72a(10) =-120a(11) =13a(12) =170a(13) =-150a(14) =-24a(15) =205a(16) =-288a(17) =-3a(18) =362a(19) =-312a(20) =50a(21) =360a(22) =-528a(23) =-51a(24) =601a(25) =-510a(26) =1a(27) =650a(28) =-840a(29) =72