A014241 ((n+1)st Fibonacci number) - (n-th nonFibonacci number).

-3, -4, -4, -4, -2, 2, 9, 20, 40, 73, 127, 215, 358, 590, 965, 1574, 2560, 4156, 6739, 10919, 17683, 28628, 46338, 74994, 121361, 196385, 317776, 514193, 832003, 1346231, 2178270, 3524538, 5702846, 9227423