A089239 - OEIS

A089239

Triangle read by rows: T(n,k) (n >= 0, 0 <= k <= n) giving number of solutions to the n-box stacking problem in which exactly k boxes are used in the stack.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 9, 3, 0, 1, 6, 15, 17, 7, 0, 0, 1, 7, 21, 28, 14, 1, 0, 0, 1, 8, 28, 43, 25, 3, 0, 0, 0, 1, 9, 36, 62, 41, 7, 0, 0, 0, 0, 1, 10, 45, 86, 63, 13, 0, 0, 0, 0, 0, 1, 11, 55, 115, 93, 23, 0, 0, 0, 0, 0, 0, 1, 12, 66, 150, 132, 37, 0

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OFFSET

0,5

COMMENTS

Given n+1 boxes labeled 0..n, such that box i weighs i grams and can support a total weight of i grams, T(n,k) = number of ways to form a stack of boxes such that no box is squashed.

LINKS

Table of n, a(n) for n=0..84.

N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.

EXAMPLE

Triangle begins:

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 9 3 0

1 6 15 17 7 0 0

1 7 21 28 14 1 0 0