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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, 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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Dec 14 2003
STATUS
approved

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Last modified February 21 20:41 EST 2024. Contains 370237 sequences. (Running on oeis4.)