a(n) = Fibonacci(2*n) - n - 1.

Terms

a(0) =0a(1) =4a(2) =16a(3) =49a(4) =137a(5) =369a(6) =978a(7) =2574a(8) =6754a(9) =17699a(10) =46355a(11) =121379a(12) =317796a(13) =832024a(14) =2178292a(15) =5702869a(16) =14930333a(17) =39088149a(18) =102334134a(19) =267914274a(20) =701408710a(21) =1836311879a(22) =4807526951a(23) =12586268999a(24) =32951280072a(25) =86267571244a(26) =225851433688a(27) =591286729849