Journal of Integer Sequences, Vol. 16 (2013), Article 13.3.1

On a Conjecture of Andrica and Tomescu


Blair D. Sullivan
Oak Ridge National Laboratory
1 Bethel Valley Road
Oak Ridge, TN 37831
USA

Abstract:

For positive integers n congruent to 0 or 3 (mod 4), let S(n) be the coefficient of xn(n+1)/4 in the expansion of $(1+x)(1+x^2)\cdots (1+x^n)$ We prove a conjecture of Andrica and Tomescu that S(n) is asymptotically equal to $\sqrt{{6 \over \pi}}\cdot 2^n \cdot n^{-3/2}$.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequence A025591.)

Received September 18 2008; revised version received September 14 2012; February 14 2013. Published in Journal of Integer Sequences, March 2 2013.

Return to Journal of Integer Sequences home page