A closed formula for the number of inequivalent ordered integer quadrilaterals with fixed perimeter

Author(s):

Bouroubi Sadek *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
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

Language:
English
Published:
Transactions on Combinatorics, Volume:13 Issue: 4, Dec 2024
Pages:
327 to 334
https://www.magiran.com/p2662572