{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:27Z","timestamp":1753893867328,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $(s_2(n))_{n=0}^\\infty$ denote Stern's diatomic sequence. For $n\\geq 2$, we may view $s_2(n)$ as the number of partitions of $n-1$ into powers of $2$ with each part occurring at most twice. More generally, for integers $b,n\\geq 2$, let $s_b(n)$ denote the number of partitions of $n-1$ into powers of $b$ with each part occurring at most $b$ times. Using this combinatorial interpretation of the sequences $s_b(n)$, we use the transfer-matrix method to develop a means of calculating $s_b(n)$ for certain values of $n$. This then allows us to derive upper bounds for $s_b(n)$ for certain values of $n$. In the special case $b=2$, our bounds improve upon the current upper bounds for the Stern sequence. In addition, we are able to prove that $\\displaystyle{\\limsup_{n\\rightarrow\\infty}\\frac{s_b(n)}{n^{\\log_b\\phi}}=\\frac{(b^2-1)^{\\log_b\\phi}}{\\sqrt 5}}$.<\/jats:p>","DOI":"10.37236\/5342","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:09:42Z","timestamp":1578686982000},"source":"Crossref","is-referenced-by-count":1,"title":["Upper Bounds for Stern's Diatomic Sequence and Related Sequences"],"prefix":"10.37236","volume":"23","author":[{"given":"Colin","family":"Defant","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,10,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:11:35Z","timestamp":1579237895000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i4p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,14]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/5342","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,10,14]]},"article-number":"P4.8"}}