a(n) = J(n) if n odd, or 4*J(n) if n even, where J = Jacobsthal numbers A001045.

Terms

a(0) =0a(1) =1a(2) =4a(3) =3a(4) =20a(5) =11a(6) =84a(7) =43a(8) =340a(9) =171a(10) =1364a(11) =683a(12) =5460a(13) =2731a(14) =21844a(15) =10923a(16) =87380a(17) =43691a(18) =349524a(19) =174763a(20) =1398100a(21) =699051a(22) =5592404a(23) =2796203a(24) =22369620a(25) =11184811a(26) =89478484a(27) =44739243a(28) =357913940a(29) =178956971