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 A090631 Given n boxes labeled 1..n, such that box i weighs 2i grams and can support a total weight of i grams; a(n) = number of stacks of boxes that can be formed such that no box is squashed. 3

%I

%S 1,2,4,6,9,12,17,22,29,36,45,54,66,78,93,108,126,144,167,190,218,246,

%T 279,312,352,392,439,486,540,594,657,720,792,864,945,1026,1119,1212,

%U 1317,1422,1539,1656,1788,1920,2067,2214,2376,2538,2718,2898,3096,3294

%N Given n boxes labeled 1..n, such that box i weighs 2i grams and can support a total weight of i grams; a(n) = number of stacks of boxes that can be formed such that no box is squashed.

%H Oystein J. Rodseth, <a href="https://doi.org/10.1016/j.disc.2006.03.051">Sloane's box stacking problem</a>, Discrete Math. 306 (2006), no. 16, 2005-2009.

%H N. J. A. Sloane and J. A. Sellers, <a href="https://doi.org/10.1016/j.disc.2004.11.014">On non-squashing partitions</a>, Discrete Math., 294 (2005), 259-274.

%F G.f.: 1/(1-q)^2/Product_{i>=0} (1 - q^(2*3^i)). - _James A. Sellers_, Dec 23 2005

%e The a(4) = 9 possible stacks are: empty, 1, 2, 3, 4, 12, 13, 14, 24.

%p p:=1/(1-q)^2/product((1-q^(2*3^i)), i=0..5): s:=series(p,q,100): for n from 0 to 99 do printf(`%d,`, coeff(s,q,n)) od: # _James A. Sellers_, Dec 23 2005

%Y Cf. A089054, A090632.

%K nonn,changed

%O 0,2

%A _N. J. A. Sloane_, Dec 13 2003

%E More terms from _James A. Sellers_, Dec 23 2005

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