On the restricted partition function via determinants with Bernoulli polynomials. II

Abstract

Let $r\ge 1$ be an integer, $\mathbf{a}=(a_1,\dots ,a_r)$ a vector of positive integers and let $D\ge 1$ be a common multiple of $a_1,\dots ,a_r$. In a continuation of a previous paper we prove that, if $D=1$ or $D$ is a prime number, the restricted partition function $p_{\mathbf{a}}(n):=$ the number of integer solutions $(x_1,\dots ,x_r)$ to ${\sum }_{j=1}^r{a}_j{x}_j=n$ with $x_1\ge 0,\dots ,x_r\ge 0$ can be computed by solving a system of linear equations with coefficients which are values of Bernoulli polynomials and Bernoulli Barnes numbers.

9 pages, minor changes

References in corpus (1)

• On the restricted partition function via determinants with Bernoulli polynomials

Cited by in corpus (1)

• Determinants with Bernoulli polynomials and the restricted partition function