Bouroubi Sadek - Faculty of Mathematics, University of Sciences and Technology Houari Boumediene, P.B. ۳۲ El-Alia, ۱۶۱۱۱, Bab Ezzouar Algiers, Algeria

Given an integer n\geq۴, 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:\[Q(n)=\left\{ \dfrac{۱}{۵۷۶}n\left( n+۳\right) \left( ۲n+۳\right) -\dfrac{\left( -۱\right) ^{n}}{۱۹۲}n\left( n-۵\right) \right\} \cdot\]

Integer quadrilaterals, Ordered quadrilaterals, Integer partitions, generating function