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A089239
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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.
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2
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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; internal format)
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OFFSET
| 0,5
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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.
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LINKS
| N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.
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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
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CROSSREFS
| Row sums give A089055. Columns give A000217, A005744, A089240.
Sequence in context: A095142 A180171 A140822 * A061676 A180182 A095145
Adjacent sequences: A089236 A089237 A089238 * A089240 A089241 A089242
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KEYWORD
| nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 11 2003
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