{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:00Z","timestamp":1753893780717,"version":"3.41.2"},"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>A set or sequence $U$ in the natural numbers is defined to be avoidable if ${\\bf N}$ can be partitioned into two sets $A$ and $B$ such that no element of $U$ is the sum of two distinct elements of $A$ or of two distinct elements of $B$. In 1980, Hoggatt [5] studied the Tribonacci sequence $T=\\{t_n\\}$ where $t_1=1$, $t_2=1$, $t_3=2$, and $t_n=t_{n-1}+t_{n-2}+t_{n-3}$ for $n\\ge 4$, and showed that it was avoidable. Dumitriu [3] continued this research, investigating Tribonacci sequences with arbitrary initial terms, and achieving partial results. In this paper we give a complete answer to the question of when a generalized Tribonacci sequence is avoidable.<\/jats:p>","DOI":"10.37236\/1531","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:02:40Z","timestamp":1578708160000},"source":"Crossref","is-referenced-by-count":1,"title":["A Complete Categorization of When Generalized Tribonacci Sequences Can Be Avoided by Additive Partitions"],"prefix":"10.37236","volume":"7","author":[{"given":"Mike","family":"Develin","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,10,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r53\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r53\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:21:42Z","timestamp":1579324902000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,10,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1531","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,10,9]]},"article-number":"R53"}}