The p-Frobenius Number for the Triple of the Generalized Star Numbers

In this paper, we give closed-form expressions of the p-Frobenius number for the triple of the generalized star numbers $a n(n-1)+1$ for an integer a≥ 4. When $a=6$, it is reduced to the famous star number. For the set of given positive integers ₁,a₂,,aₖ\, the p-Frobenius number is the largest integer N whose number of nonnegative integer representations N=a₁ x₁+a₂ x₂++aₖ xₖ is at most p. When $p=0$, the $0$-Frobenius number is the classical Frobenius number, which is the central topic of the famous linear Diophantine problem of Frobenius.