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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.

%I A090641 #5 Mar 30 2012 16:49:51
%S A090641 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,
%T A090641 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,
%U A090641 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
%N 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.
%C A090641 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.
%H A090641 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 A090641 Triangle begins:
%e A090641 1
%e A090641 1 1
%e A090641 1 2 1
%e A090641 1 3 3 1
%e A090641 1 4 6 3 0
%e A090641 1 5 10 7 0 0
%Y A090641 Row sums of A089054. Columns give A000217, etc.
%K A090641 nonn,tabl
%O A090641 0,5
%A A090641 _N. J. A. Sloane_, Dec 14 2003