a(n) = floor((Fibonacci(2*n+1)+1)/2).

Terms

a(0) =1a(1) =1a(2) =3a(3) =7a(4) =17a(5) =45a(6) =117a(7) =305a(8) =799a(9) =2091a(10) =5473a(11) =14329a(12) =37513a(13) =98209a(14) =257115a(15) =673135a(16) =1762289a(17) =4613733a(18) =12078909a(19) =31622993a(20) =82790071a(21) =216747219a(22) =567451585a(23) =1485607537a(24) =3889371025a(25) =10182505537a(26) =26658145587a(27) =69791931223a(28) =182717648081a(29) =478361013021