Abstract
Let a(n) be the Stern 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. We also derive a formula expressing the same polynomials in terms of sets of increasing integers of alternating parity and derive a determinant representation for a(n).
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