A080889 Expansion of 1/(1+Sum_{k>0} (-x)^Fibonacci(k)).

1, 2, 3, 5, 9, 17, 32, 59, 107, 194, 354, 648, 1186, 2169, 3964, 7243, 13237, 24196, 44230, 80849, 147780, 270117, 493731, 902469, 1649589, 3015219, 5511391, 10074030, 18413879, 33657935, 61521899, 112453248, 205548470, 375713217