  Let a(n) be the Stern's diatomic sequence, and let x1,...,xr be the distances
between successive 1's in the binary expansion of the (odd) positive integer n.
We show that a(n) is obtained by evaluating generalized Chebyshev polynomials
when the variables are given the values x1+1, ..., xr+1, and we derive a
formula expressing the same polynomials in terms of sets of increasing integers
of alternating parity. We also show that a(n) = Det(Ir + Mr), where Ir is the
rxr identity matrix, and Mr is the rxr matrix that has x1,...,xr along the main
diagonal, then all 1's just above and below the main diagonal, and all the
other entries are 0.
