A014242 (n-th Fibonacci number that is not 1) - (n-th number that is 1 or not a Fibonacci number).

1, -1, -1, 1, 4, 11, 23, 43, 75, 129, 217, 360, 592, 968, 1577, 2562, 4158, 6741, 10921, 17685, 28630, 46340, 74996, 121363, 196387, 317779, 514196, 832005, 1346233, 2178272, 3524540, 5702848, 9227425