<?xml version="1.0" encoding="UTF-8"?><OAI-PMH xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/ http://www.openarchives.org/OAI/2.0/OAI-PMH.xsd"><responseDate>2026-10-19T00:37:25Z</responseDate><request verb="GetRecord" identifier="oai:ebyu-rdlopen.rawdatalibrary.net:ebyu/16959" metadataPrefix="oai_dc">https://ebyu-rdlopen.rawdatalibrary.net/oai/request</request><GetRecord><record><header><identifier>oai:ebyu-rdlopen.rawdatalibrary.net:ebyu/16959</identifier><datestamp>2026-10-18T20:41:10Z</datestamp><setSpec>openaire</setSpec><setSpec>driver</setSpec><setSpec>com_ebyu_10000</setSpec><setSpec>col_ebyu_10001</setSpec></header><metadata><oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd"><dc:title>Discatenated and lacunary recurrences</dc:title><dc:creator>Akkus, Hakan</dc:creator><dc:creator>Deveci, Omur</dc:creator><dc:creator>Ozkan, Engin</dc:creator><dc:creator>Shannon, Anthony G.</dc:creator><dc:subject>Fibonacci numbers</dc:subject><dc:subject>Lucas sequences</dc:subject><dc:subject>Lacunary</dc:subject><dc:subject>Primordial sequences</dc:subject><dc:subject>Recurrence relations</dc:subject><dc:subject>FORMULAS</dc:subject><dc:subject>Mathematics</dc:subject><dc:description>Recursive sequences with gaps have been studied previously. This paper considers some elementary properties of such sequences where the gaps have been created on a regular basis from sequence to sequence - 'discatenated' (systematic gaps) and 'lacunary' (general gaps). In particular, their generating functions are developed in order to open up their general terms and relations with other properties.</dc:description><dc:publisher>BULGARIAN ACAD SCIENCE</dc:publisher><dc:date>2024</dc:date><dc:type>Article</dc:type><dc:identifier>https://rdlopen.rawdatalibrary.net/r/ebyu/16959</dc:identifier><dc:identifier>https://doi.org/10.7546/nntdm.2024.30.1.8-19</dc:identifier><dc:identifier>1310-5132</dc:identifier><dc:language>en</dc:language><dc:relation>NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS</dc:relation><dc:rights>info:eu-repo/semantics/openAccess</dc:rights><dc:type>info:eu-repo/semantics/article</dc:type><dc:identifier>https://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/16959</dc:identifier></oai_dc:dc></metadata></record></GetRecord></OAI-PMH>