On a Conjecture of Andrica and Tomescu

2012/10/31 by Blair D. Sullivan, Sullivan, Blair D. · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Theories #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1210.8437

openalex publication_date 2012/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S(n) be the integer sequence which is the coefficient of x^n(n+1)/4 in the expansion of (1+x)(1+x²), ..., (1+xⁿ) for positive integers n congruent to 0 or 3 mod 4. We prove a conjecture of Andrica and Tomescu that S(n) is asymptotic to √(6/π) 2ⁿ n^-3/2 as n approaches infinity.

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