{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T17:16:53Z","timestamp":1764782213606,"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>We present a method to obtain congruences modulo powers of $2$ for sequences given by recurrences of finite depth with polynomial coefficients. We apply this method to Catalan numbers, Fu\u00df--Catalan numbers, and to subgroup counting functions associated with Hecke groups and their lifts. This leads to numerous new results, including many extensions of known results to higher powers of $2$. <\/jats:p>","DOI":"10.37236\/2433","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:36:11Z","timestamp":1578713771000},"source":"Crossref","is-referenced-by-count":8,"title":["A Method for Determining the Mod-$2^k$ Behaviour of Recursive Sequences, with Applications to Subgroup Counting"],"prefix":"10.37236","volume":"18","author":[{"given":"M.","family":"Kauers","sequence":"first","affiliation":[]},{"given":"C.","family":"Krattenthaler","sequence":"additional","affiliation":[]},{"given":"T. W.","family":"M\u00fcller","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,6,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i2p37\/pdf_com","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i2p37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:33:19Z","timestamp":1579300399000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i2p37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,20]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2011,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/2433","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,6,20]]},"article-number":"P37"}}