On the average of triangular numbers

dc.creatorCatalani, Mario
dc.date2003-04-13
dc.date.accessioned2026-07-07T04:56:49Z
dc.date.available2026-07-07T04:56:49Z
dc.descriptionThe problem we are dealing with is the following: find two sequences $a_n$ and $b_n$ such that the average of the first $b_n$ triangular numbers (starting with the triangular number 1) is still a triangular number, precisely the $a_n$-th triangular number. We get also some side results: for instance one of the sequence instrumental to finding the asked for sequences turns out to be a bisection of the sequence of the numerators of continued fraction convergents to $\sqrt{3}$.
dc.descriptionFixed some minor typos
dc.identifierhttps://arxiv.org/abs/math/0304160
dc.identifierhttp://arxiv.org/abs/math/0304160
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67059
dc.subjectNumber Theory
dc.subjectCombinatorics
dc.subject11A99; 11A55
dc.titleOn the average of triangular numbers
dc.typetext

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