Congruences modulo high powers of 2 for sloane's box stacking function

Øystein J. Rødseth, James A. Sellers

Research output: Contribution to journalArticlepeer-review


We are given n boxes, labeled 1, 2,..., n. Box i weighs i grams and can support a total weight of i grams. The number of different ways to build a single stack of boxes in which no box will be squashed by the weight of the boxes above it is denoted by f(n). In a 2006 paper, the first author asked for "congruences for f(n) modulo high powers of 2". In this note, we accomplish this task by proving that, for r ≥ 5 and all n ≥ 0, f(2 rn) - f(2r-1n) ≡ 0 (mod 2r), and that this result is "best possible". Some additional complementary congruence results are also given.

Original languageEnglish (US)
Pages (from-to)255-263
Number of pages9
JournalAustralasian Journal of Combinatorics
StatePublished - Jun 1 2009
Externally publishedYes


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