p-Numerical Semigroups of Generalized Fibonacci Triples

For a nonnegative integer p, we give explicit formulas for the p-Frobenius number and p-genus of generalized Fibonacci numerical semigroups. Here, p-numerical semigroup Sp is defined as set integers whose integral linear combinations given positive a1,a2,…,ak are expressed in more than p ways. When p=0, S0 with 0-Frobenius 0-genus original Frobenius genus. In this paper, consider involving Jacobsthal polynomials, which include numbers special cases. We can also deal Jacobsthal–Lucas including Lucas accordingly. An application on p-Hilbert series provided. There some interesting connections between geometric algebraic structures that exhibit symmetry properties.