On 5-regular bipartitions with even parts distinct

In 2010, Andrews, Michael D. Hirschhorn and James A. Sellers considered the function ped(n), the number of partition of an integer n with even parts distinct (the odd parts are unrestricted). They obtained infinite families of congruences in the spirit of Ramanujan’s congruences for the unrestricted partition function p(n). Let b(n) denote the number of 5-regular bipartitions of a positive integer n with even parts distinct (odd parts are unrestricted). In this paper, we establish many infinite families of congruences modulo powers of 2 for b(n). For example, ∑n=0∞b16·32α·52βn+14·32α·52β+1qn≡8f23f53(mod16),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \sum _{n=0}^{\infty } b\left(16\cdot 3^{2\alpha }\cdot 5^{2\beta }n+14\cdot 3^{2\alpha }\cdot 5^{2\beta }+1\right) q^n \equiv 8f_2^3f_5^3 \pmod {16} , \end{aligned}$$\end{document}where α,β≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha , \beta \ge 0$$\end{document}.