The Frobenius number for the triple of the 2-step star numbers

Abstract

In this paper, we give closed form expressions of the Frobenius number for the triple of the $2$-step star numbers $an(n-2)+1$ for an integer $a\ge 4$. These numbers have been studied from different aspects for some $a$'s. These numbers can also be considered as variations of the well known star numbers of the form $6n(n-1)+1$. We also give closed form expressions of the Sylvester number (genus) for the triple of the $2$-step star numbers.