https://orcid.org/0000-0001-8744-2298
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Abstract
We consider linear recursions of length two and related gap recursions where the indices may not be consecutive integers. Given a linear recursion of length two, we prove the existence of an explicit linear recursion of length with arbitrary distance between indices. Conversely, it is shown under some mild assumption that a linear recursion of length
can be reduced to one of length two.
Acknowledgments
The authors are grateful to the anonymous referee for her or his valuable comments and corrections. The authors would like to thank National Research Council of Thailand (NRCT) and Walailak University for facilities and financial supports.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
This work was supported by the National Research Council of Thailand (NRCT) and Walailak University under Grant number NRCT5-RSA63019-06 (2563NRCT322800).