On Robbins' example of a continued fraction expansion for a quartic power series over F13

The continued fraction expansion for a quartic power series over the finite field F13 was conjectured first in [W. Mills, D. Robbins, Continued fractions for certain algebraic power series, J. Number Theory 23 (1986) 388–404] and later in a more precise way in [W. Buck, D. Robbins, The continued fraction of an algebraic power series satisfying a quartic equation, J. Number Theory 50 (1995) 335–344]. Here this conjecture is proved by describing the continued fraction expansion for a large family of algebraic power series over a finite field.