A closed formula for the number of inequivalent ordered integer quadrilaterals with fixed perimeter
نویسندگان
1 Faculty of Mathematics, University of Sciences and Technology Houari Boumediene, P.B. 32 El-Alia, 16111, Bab Ezzouar Algiers, Algeria
doi
10.22108/toc.2023.136913.2045چکیده
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:\[Q(n)=\left\{ \dfrac{1}{576}n\left( n+3\right) \left( 2n+3\right) -\dfrac{\left( -1\right) ^{n}}{192}n\left( n-5\right) \right\} \cdot\]
