Stern's Diatomic Series

Stern's diatomic series is the sequence

(1)

... (OEIS A002487) which arises in the Calkin-Wilf tree. It is sometimes also known as the fusc function (Dijkstra 1982).

The th term can be given by the recurrence equation

(2)

with  and . A sum formula is given by

(3)

A generating function is given by

			(4)
			(5)

REFERENCES:

Calkin, N. and Wilf, H. S. "Recounting the Rationals." Amer. Math. Monthly 107, 360-363, 2000.

Dijkstra, E. W. Selected Writings on Computing: A Personal Perspective. New York: Springer-Verlag, pp. 215-232, 1982.

Gibbons, L.; Lester, D.; and Bird, R. "Functional Pearl: Enumerating the Rationals." J. Func. Prog. 16, 281-291, 2006.

Sloane, N. J. A. Sequence A002487/M0141 in "The On-Line Encyclopedia of Integer Sequences."