Congruences modulo powers of 2 for generalized Frobenius partitions with six colors

A generalized Frobenius partition of Formula: see text with Formula: see text colors is a two-rowed array Formula: see text where Formula: see text, and the integer entries are taken from Formula: see text distinct copies of the non-negative integers distinguished by color, and the rows are ordered first by size and then by color with no two consecutive like entries in any row. Let Formula: see text denote the number of this kind of partitions of Formula: see text with Formula: see text colors. In this paper, we establish some congruences modulo powers of 2 for Formula: see text.