a(n) = (2^n + 3 - 7*(-1)^n + 3*0^n)/6; or a(0) = 0 and for n > 0, a(n) = A005578(n-1) - (-1)^n.

Terms

a(0) =0a(1) =2a(2) =0a(3) =3a(4) =2a(5) =7a(6) =10a(7) =23a(8) =42a(9) =87a(10) =170a(11) =343a(12) =682a(13) =1367a(14) =2730a(15) =5463a(16) =10922a(17) =21847a(18) =43690a(19) =87383a(20) =174762a(21) =349527a(22) =699050a(23) =1398103a(24) =2796202a(25) =5592407a(26) =11184810a(27) =22369623a(28) =44739242a(29) =89478487