  We introduce and study a cyclically invariant polynomial which is an analog
of the classical tridiagonal determinant usually called the continuant. We
prove that this polynomial can be calculated as the Pfaffian of a
skew-symmetric matrix. We consider the corresponding Diophantine equation and
prove an analog of a famous result due to Conway and Coxeter. We also observe
that Chebyshev polynomials of the first kind arise as Pfaffians.
