Stern,s Diatomic Series
المؤلف:
Calkin, N. and Wilf, H. S.
المصدر:
"Recounting the Rationals." Amer. Math. Monthly 107
الجزء والصفحة:
...
5-11-2020
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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
![a_n=<span style=]() {a_(n/2) for n even; a_((n-1)/2)+a_((n+1)/2) for n odd " src="https://mathworld.wolfram.com/images/equations/SternsDiatomicSeries/NumberedEquation2.gif" style="height:44px; width:205px" /> |
(2)
|
with 
and 
. A sum formula is given by
 |
(3)
|
A generating function is given by
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."
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