Discatenated and lacunary recurrences
Hakan Akkuş, Ömür Deveci, Engi̇n Özkan, Anthony G. Shannon · Notes on Number Theory and Discrete Mathematics · 2024
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.