Congruences modulo powers of 2 and 3 for a restricted binary partition function a la Andrews and Lewis

Abstract

Let $W(n)$ denote the number of partitions of $n$ into powers of 2 such that for all $i\geq 0$, $2^{2i}$ and $2^{2i+1}$ cannot both be parts of a particular partition. Recently,  Lan and Sellers proved  a number of congruences modulo 2, 3 and 4. In this note,  we prove a number of Ramanujan-type congruences modulo powers of 2 and 3.