A090641 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, 3, 0, 1, 5, 10, 7, 0, 0, 1, 6, 15, 13, 1, 0, 0, 1, 7, 21, 22, 3, 0, 0, 0, 1, 8, 28, 34, 7, 0, 0, 0, 0, 1, 9, 36, 50, 13, 0, 0, 0, 0, 0, 1, 10, 45, 70, 23, 0, 0, 0, 0, 0, 0, 1, 11, 55, 95, 37, 0, 0, 0, 0, 0, 0, 0, 1, 12, 66, 125, 57, 1, 0, 0, 0

Offset

0,5

Comments

Given n boxes labeled 1..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..86.

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

Example

Triangle begins:
1
1 1
1 2 1
1 3 3 1
1 4 6 3 0
1 5 10 7 0 0

Crossrefs

Row sums of A089054. Columns give A000217, etc.

Sequence in context: A157283 A067049 A349976 * A055216 A216236 A217770

Adjacent sequences: A090638 A090639 A090640 * A090642 A090643 A090644

Keyword

nonn,tabl

Author

N. J. A. Sloane, Dec 14 2003

Status

approved