For Fibonacci sequence, x = 1x^1 x * g(x) = 1x^2 + 1x^3 + 2x^4 + 3x^5 + 5x^6 + ... + x^2 * g(x) = 1x^3 + 1x^4 + 2x^5

For Fibonacci sequence, x = 1x^1 x * g(x) = 1x^2 + 1x^3 + 2x^4 + 3x^5 + 5x^6 + ... + x^2 * g(x) = 1x^3 + 1x^4 + 2x^5 + 3x^6 + ... ------------------------------------------------------------ = g(x) = 1x^1 + 1x^2 + 2x^3 + 3x^4 + 5x^5 + 8x^6 + ... Hence, x = (1 - x - x^2) * g(x) g(x) = x / (1 - x - x^2)