a(n) = 5*2^n/9 + 1/4 + (-1)^n*(n/6 + 7/36).

Terms

a(0) =1a(1) =1a(2) =3a(3) =4a(4) =10a(5) =17a(6) =37a(7) =70a(8) =144a(9) =283a(10) =571a(11) =1136a(12) =2278a(13) =4549a(14) =9105a(15) =18202a(16) =36412a(17) =72815a(18) =145639a(19) =291268a(20) =582546a(21) =1165081a(22) =2330173a(23) =4660334a(24) =9320680a(25) =18641347a(26) =37282707a(27) =74565400a(28) =149130814a(29) =298261613