@article {
author = {Sadek, Bouroubi},
title = {A closed formula for the number of inequivalent ordered integer quadrilaterals with fixed perimeter},
journal = {Transactions on Combinatorics},
volume = {13},
number = {4},
pages = {327-334},
year = {2024},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2023.136913.2045},
abstract = {Given an integer $n\geq4$, how many inequivalent quadrilaterals with ordered integer sides and perimeter $n$ are there? Denoting such number by $Q(n)$, the answer is given by the following closed formula:\[Q(n)=\left\{ \dfrac{1}{576}n\left( n+3\right) \left( 2n+3\right) -\dfrac{\left( -1\right) ^{n}}{192}n\left( n-5\right) \right\} \cdot\]},
keywords = {Integer quadrilaterals,Ordered quadrilaterals,Integer partitions,generating function},
url = {https://toc.ui.ac.ir/article_27710.html},
eprint = {https://toc.ui.ac.ir/article_27710_0ca238274568bdcd23686f2944f7e43b.pdf}
}