  In Oste and Van der Jeugt, SIGMA, 12 (2016) we classified all pairs of
recurrence relations in which two (dual) Hahn polynomials with different
parameters appear. Such pairs are referred to as (dual) Hahn doubles, and the
same technique was then applied to obtain all Racah doubles. We now consider a
special case concerning the doubles related to Racah polynomials. This gives
rise to an interesting class of two-diagonal matrices with closed form
expressions for the eigenvalues. Just as it was the case for (dual) Hahn
doubles, the resulting two-diagonal matrix can be used to construct a finite
oscillator model. We discuss some properties of this oscillator model, give its
(discrete) position wavefunctions explicitly, and illustrate their behaviour by
means of some plots.
