(1) Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, 5008 Bergen, Norway;(2) Department of Mathematics, Penn State University, University Park, PA 16802, USA
Abstract:
A partition with is non-squashing if On their way towards the solution of a certain box-stacking problem, Sloane and Sellers were led to consider the number b(n) of non-squashing partitions of n into distinct parts. Sloane and Sellers did briefly consider congruences for b(n) modulo 2. In this paper we show that 2r-2 is the exact power of 2 dividing the difference b(2r+1n)–b(2r-1n) for n odd and r 2.
with
is non-squashing if
On their way towards the solution of a certain box-stacking problem, Sloane and Sellers were led to consider the number b(n) of non-squashing partitions of n into distinct parts. Sloane and Sellers did briefly consider congruences for b(n) modulo 2. In this paper we show that 2r-2 is the exact power of 2 dividing the difference b(2r+1n)–b(2r-1n) for n odd and r 
2.