2017/10/16 by Jia Huang, Huang, Jia, Madison Mickey +3
Computer Science · Mathematics · #05A15 #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics #Numerical Methods and Algorithms #math.CO #msc:05A15
paper · pdf · doi:10.48550/arxiv.1710.05651
arxiv created 2017/10/16 · openalex publication_date 2017/10/16 · arxiv updated 2017/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The sequence A000975 in OEIS can be defined by A1=1, An+1=2An if n is odd, and An+1=2An+1 if n is even. This sequence satisfies other recurrence relations, admits some closed formulas, and is known to enumerate several interesting families of objects. We provide a new interpretation of this sequence using a binary operation defined by a\ominus b := -a -b. We show that the number of distinct results obtained by inserting parentheses in the expression x0\ominus x1\ominus ⋯\ominus xn equals An, by investigating the leaf depth in binary trees. Our result can be viewed as a quantitative measurement for the nonassociativity of the binary operation \ominus.