a(n) = (1/9)*(7*2^n + (-1)^n*(3*n+2)) - (n-1)^2.

Terms

a(0) =0a(1) =1a(2) =3a(3) =1a(4) =5a(5) =7a(6) =27a(7) =61a(8) =153a(9) =331a(10) =719a(11) =1489a(12) =3069a(13) =6223a(14) =12579a(15) =25285a(16) =50753a(17) =101683a(18) =203607a(19) =407449a(20) =815205a(21) =1630711a(22) =3261803a(23) =6523981a(24) =13048425a(25) =26097307a(26) =52195167a(27) =104390881a(28) =208782413a(29) =417565471