{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T16:12:46Z","timestamp":1774627966555,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In their study of a quartic integral, Boros and Moll discovered a special class of sequences, which is called the Boros\u2013Moll sequences. In this paper, we consider the\u00a0concavity and convexity of the Boros\u2013Moll\u00a0sequences $\\{d_i(m)\\}_{i=0}^m$. We show that for any integer $m\\geq\u00a06$, there exist two positive\u00a0 integers $t_0(m)$ and $t_1(m)$\u00a0 such that $d_i(m)+d_{i+2}(m)&gt;2d_{i+1}(m)$\u00a0 for $i\\in [0,t_0(m)]\\bigcup[t_1(m),m-2]$\u00a0 and $d_i(m)+d_{i+2}(m) &lt; 2d_{i+1}(m)$\u00a0\u00a0 for $i\\in [t_0(m)+1,t_1(m)-1]$. When $m$ is a square, we find\u00a0 $t_0(m)=\\frac{m-\\sqrt{m}-4}{2}$ and $t_1(m)\u00a0 =\\frac{m+\\sqrt{m}-2}{2}$. As a corollary of our results, we\u00a0 show that\u00a0\\[\\lim_{m\\rightarrow +\\infty }\\frac{{\\rm card}\\{i|d_i(m)+d_{i+2}(m)&lt; 2d_{i+1}(m), 0\\leq i \\leq m-2\\}}{\\sqrt{m}}=1.\u00a0\\]<\/jats:p>","DOI":"10.37236\/3829","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:33:25Z","timestamp":1578702805000},"source":"Crossref","is-referenced-by-count":1,"title":["The Concavity and Convexity of the Boros-Moll Sequences"],"prefix":"10.37236","volume":"22","author":[{"given":"Ernest X.W.","family":"Xia","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,1,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:38:52Z","timestamp":1579257532000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/3829","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1,9]]},"article-number":"P1.8"}}