a(n) = ((6*n + 10)/27)*2^(n-1) + ((-1)^(n-1))*(6*n + 5)/27.

Terms

a(0) =1a(1) =1a(2) =5a(3) =9a(4) =25a(5) =53a(6) =125a(7) =273a(8) =609a(9) =1325a(10) =2885a(11) =6217a(12) =13353a(13) =28517a(14) =60685a(15) =128641a(16) =271857a(17) =572829a(18) =1203925a(19) =2524345a(20) =5281721a(21) =11029461a(22) =22991005a(23) =47846129a(24) =99420545a(25) =206297613a(26) =427508325a(27) =884842793a(28) =1829337929a(29) =3777980485