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%I #5 Mar 30 2012 16:49:50
%S 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,
%T 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,
%U 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
%N 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.
%C 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.
%H N. J. A. Sloane and J. A. Sellers, <a href="http://arXiv.org/abs/math.CO/0312418">On non-squashing partitions</a>, Discrete Math., 294 (2005), 259-274.
%e Triangle begins:
%e 1
%e 1 1
%e 1 2 1
%e 1 3 3 1
%e 1 4 6 4 1
%e 1 5 10 9 3 0
%e 1 6 15 17 7 0 0
%e 1 7 21 28 14 1 0 0
%Y Row sums give A089055. Columns give A000217, A005744, A089240.
%K nonn,tabl
%O 0,5
%A _N. J. A. Sloane_, Dec 11 2003
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