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A089054
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Solution to the non-squashing boxes problem (version 1).
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7
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1, 2, 4, 8, 14, 23, 36, 54, 78, 109, 149, 199, 262, 339, 434, 548, 686, 849, 1043, 1269, 1535, 1842, 2199, 2607, 3078, 3613, 4225, 4915, 5700, 6581, 7576, 8686, 9934, 11321, 12871, 14585, 16493, 18596, 20925, 23481, 26303, 29392, 32788, 36492, 40553, 44972, 49799
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OFFSET
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0,2
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COMMENTS
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Given n boxes labeled 1..n, such that box i weighs i 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.
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LINKS
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N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, arXiv:math/0312418 [math.CO], 2003; Discrete Math., 294 (2005), 259-274.
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FORMULA
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G.f.: (B(x)-x)/(1-x)^2, where B(x) = g.f. for A088567.
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MATHEMATICA
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max = 50; B[x_] = 1+x/(1-x) + Sum[x^(3 2^(k-1))/Product[(1-x^(2^j)), {j, 0, k}], {k, 1, Log[2, max]}] + O[x]^max;
A[x_] = (B[x]-x)/(1-x)^2;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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