On the lacunary sum of trinomial coefficients

He-Xia Ni and Hao Pan

Applied Mathematics and Computation, 2018, vol. 339, issue C, 286-293

Abstract: The trinomial coefficient (nk)2 is given by ∑k=−nn(nk)2xk=(1+x+x−1)n.In this paper, we obtain the explicit formulas for the lacunary sum ∑−n≤k≤nk≡r(modm)(nk)2.For example, ∑−n≤k≤nk≡1(mod12)(nk)2=2n+3n−(−1)n+6Hn12,where H0=0,H1=1 and Hn=2Hn−1+2Hn−2 for n ≥ 2.

Keywords: Trinomial coefficient; Linear recurrence sequence; Chebyshev polynomial (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300318305861
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:339:y:2018:i:c:p:286-293

DOI: 10.1016/j.amc.2018.07.028

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().