{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:37Z","timestamp":1753893817985,"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>We study the recursions $A(n) = A(n-a-A^k(n-b)) + A(A^k(n-b))$ where $a \\geq 0$, $b \\geq 1$ are integers and the superscript $k$ denotes a $k$-fold composition, and also the recursion $C(n) = C(n-s-C(n-1)) + C(n-s-2-C(n-3))$ where $s \\geq 0$ is an interger. We prove that under suitable initial conditions the sequences $A(n)$ and $C(n)$ will be defined for all positive integers, and be monotonic with their forward difference sequences consisting only of 0 and 1. We also show that the sequence generated by the recursion for $A(n)$ with parameters $(k,a,b) = (k,0,1)$, and initial conditions $A(1) = A(2) = 1$, satisfies $A(E_n) = E_{n-1}$ where $E_n$ is a generalized Fibonacci recursion defined by $E_n = E_{n-1} + E_{n-k}$ with $E_n = 1$ for $1 \\leq n \\leq k$.<\/jats:p>","DOI":"10.37236\/583","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:48:12Z","timestamp":1578714492000},"source":"Crossref","is-referenced-by-count":2,"title":["On Variants of Conway and Conolly's Meta-Fibonacci Recursions"],"prefix":"10.37236","volume":"18","author":[{"given":"Abraham","family":"Isgur","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mustazee","family":"Rahman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,4,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p96\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p96\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:12:49Z","timestamp":1579302769000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p96"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/583","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,4,29]]},"article-number":"P96"}}