a(n) = (1/3)*(1 - (-2)^n + 3*(-1)^n ) = (-1)^(n+1)*A167030(n).

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =-4a(5) =10a(6) =-20a(7) =42a(8) =-84a(9) =170a(10) =-340a(11) =682a(12) =-1364a(13) =2730a(14) =-5460a(15) =10922a(16) =-21844a(17) =43690a(18) =-87380a(19) =174762a(20) =-349524a(21) =699050a(22) =-1398100a(23) =2796202a(24) =-5592404a(25) =11184810a(26) =-22369620a(27) =44739242a(28) =-89478484a(29) =178956970