University of IsfahanTransactions on Combinatorics2251-865713420241201A closed formula for the number of inequivalent ordered integer quadrilaterals with fixed perimeter3273342771010.22108/toc.2023.136913.2045ENBouroubiSadekFaculty of Mathematics, University of Sciences and Technology Houari Boumediene, P.B. 32 El-Alia, 16111, Bab Ezzouar Algiers, Algeria0000-0002-0691-6189Journal Article20230221Given 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:<br />\[<br />Q(n)=\left\{ \dfrac{1}{576}n\left( n+3\right) \left( 2n+3\right) -\dfrac{\left( -1\right) ^{n}}{192}n\left( n-5\right) \right\} \cdot<br />\]https://toc.ui.ac.ir/article_27710_0ca238274568bdcd23686f2944f7e43b.pdf