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

Offset: 0

Author

N. J. A. Sloane, Dec 11 2003

Keywords

• nonn
• tabl

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.

Examples

			Triangle begins:
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
		

Links

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

Crossrefs

Row sums give A089055. Columns give A000217, A005744, A089240.