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A Correlation Identity for Stern's Sequence
-
Michael Coons
Published/Copyright:
May 31, 2012
Abstract.
The Stern sequence (also called Stern's diatomic sequence) is defined by the recurrence relations 
, 
, and in general by 
and 
. In this note we prove a new identity for Stern's sequence. In particular, we show that if e and a are nonnegative integers, then for any integer r with 
, we have
It seems that this is the first correlation-type identity concerning Stern's sequence in the literature.
Received: 2011-05-17
Accepted: 2011-12-05
Published Online: 2012-05-31
Published in Print: 2012-June
© 2012 by Walter de Gruyter Berlin Boston
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- On a Theorem of Prachar Involving Prime Powers
- A Novel Approach to the Discovery of Binary BBP-Type Formulas for Polylogarithm Constants
- A Recurrence Related to the Bell Numbers
- Sum-Product Estimates Applied to Waring's Problem over Finite Fields
- Communal Partitions of Integers
- On Computation of Exact van der Waerden Numbers
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- Partition of an Integer into Distinct Bounded Parts, Identities and Bounds
- A Correlation Identity for Stern's Sequence
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Articles in the same Issue
- Masthead
- On a Theorem of Prachar Involving Prime Powers
- A Novel Approach to the Discovery of Binary BBP-Type Formulas for Polylogarithm Constants
- A Recurrence Related to the Bell Numbers
- Sum-Product Estimates Applied to Waring's Problem over Finite Fields
- Communal Partitions of Integers
- On Computation of Exact van der Waerden Numbers
- On the Complexity of Chooser–Picker Positional Games
- Partition of an Integer into Distinct Bounded Parts, Identities and Bounds
- A Correlation Identity for Stern's Sequence
- Primitive Prime Divisors in Zero Orbits of Polynomials
