Let φ be the positive root to x² = x + 1. In how many ways can φ⁶ be expressed as a degree 4 polynomial in φ with nonnegative integer coefficients? For example, one way φ⁶ can be written as a degree 5 polynomial in φ with nonnegative integer coefficients is φ⁶ = φ⁵ + φ⁴.