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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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

CROSSREFS

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

Sequence in context: A140822 A212954 A299807 * A223968 A214846 A061676

Adjacent sequences:  A089236 A089237 A089238 * A089240 A089241 A089242

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Dec 11 2003

STATUS

approved

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Last modified October 14 02:29 EDT 2019. Contains 327995 sequences. (Running on oeis4.)