{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:49Z","timestamp":1753893829295,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper we develop a general method to enumerate the congruences of finite summations $\\sum_{k=0}^{p-1} \\frac{a_k}{m^k} \\!\\pmod{p}$ and $\\sum_{k=0}^{p-1-h} \\frac{a_k a_{k+h}}{B^k} \\!\\pmod{p}$ for the the infinite sequence $\\{a_n\\}_{n\\ge 0}$ with generating functions $(1+x f(x))^\\frac{N}{2}$, where $f(x)$ is an integer polynomial and $N$ is an odd integer with $|N|&lt; p$. We also enumerate the congruences of some similar finite summations involving generating functions $\\frac{1-\\alpha x -\\sqrt{1-2(\\alpha+\\beta)x + Bx^2}}{\\beta x}$ and $\\frac{1-\\alpha x-\\sqrt{1-2\\alpha x+(\\alpha^2-4\\beta)x^2}}{2\\beta x^2}$.<\/jats:p>","DOI":"10.37236\/3693","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:04:01Z","timestamp":1578686641000},"source":"Crossref","is-referenced-by-count":1,"title":["Congruences of Finite Summations of the Coefficients in certain Generating Functions"],"prefix":"10.37236","volume":"21","author":[{"given":"Po-Yi","family":"Huang","sequence":"first","affiliation":[]},{"given":"Shu-Chung","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Yeong-Nan","family":"Yeh","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,6,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p45\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p45\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:58:41Z","timestamp":1579240721000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i2p45"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6,9]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/3693","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,6,9]]},"article-number":"P2.45"}}