On the average of triangular numbers
| dc.creator | Catalani, Mario | |
| dc.date | 2003-04-13 | |
| dc.date.accessioned | 2026-07-07T04:56:49Z | |
| dc.date.available | 2026-07-07T04:56:49Z | |
| dc.description | The 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.description | Fixed some minor typos | |
| dc.identifier | https://arxiv.org/abs/math/0304160 | |
| dc.identifier | http://arxiv.org/abs/math/0304160 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67059 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11A99; 11A55 | |
| dc.title | On the average of triangular numbers | |
| dc.type | text |