Domingo Gómez Morín

This graph represent the solution to the equation:

F_n = 3F_{n - 1} + 3F_{n - 2} + F_{n - 3}

This equation connects three previous values, to the fourth one, so one needs to give three initial values. For this case I chose:

F₁ = 3 , F₂ = 15 , F₃ = 57.

The solution tends to (1 + 2^1/3 + 2^2/3)ⁿ, as n increases.

According to Gómez Morín, this equation helps us get a periodic generalized continued fraction for these cubic roots of integer coefficient polynomials.