Geodesic
Non-standard binary representations and the Stern sequence
Katie Anders1 ; Madeline Locus Dawsey1 ; Rajat Gupta2 ; Joseph Vandehey1
1University of Texas at Tyler
2University of Maine
The electronic journal of combinatorics, Tome 31 (2024) no. 4
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We show that the number of short binary signed-digit representations of an integer $n$ is equal to the $n$-th term in the Stern sequence. Various proofs are provided, including direct, bijective, and generating function proofs. We also show that this result can be derived from recent work of Monroe on binary signed-digit representations of a fixed length.
DOI : 10.37236/12312
Classification : 11B37, 11A63, 05A15
Mots-clés : Stern sequence, binary signed-digit representation

Katie Anders  1   ; Madeline Locus Dawsey  1   ; Rajat Gupta  2   ; Joseph Vandehey  1

1 University of Texas at Tyler
2 University of Maine 
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     title = {Non-standard binary representations and the {Stern} sequence},
     journal = {The electronic journal of combinatorics},
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Katie Anders; Madeline Locus Dawsey; Rajat Gupta; Joseph Vandehey. Non-standard binary representations and the Stern sequence. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12312

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