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A089054 Solution to the non-squashing boxes problem (version 1). 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

REFERENCES

Amanda Folsom, Youkow Homma, Jun Hwan Ryu, Benjamin Tong, On a general class of non-squashing partitions, Discrete Mathematics 339 (2016) 1482-1506.

Rodseth, Oystein J., Sloane's box stacking problem. Discrete Math. 306 (2006), no. 16, 2005-2009.

LINKS

Table of n, a(n) for n=0..46.

N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.

FORMULA

G.f.: (B(x)-x)/(1-x)^2, where B(x) = g.f. for A088567.

MATHEMATICA

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;

CoefficientList[A[x], x] (* Jean-Fran├žois Alcover, Sep 01 2018 *)

CROSSREFS

Cf. A000123, A088567, A089055, A090631, A090632. Row sums of A090641.

Sequence in context: A138526 A286522 A201347 * A055291 A091773 A107055

Adjacent sequences:  A089051 A089052 A089053 * A089055 A089056 A089057

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 04 2003

STATUS

approved

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Last modified September 22 08:23 EDT 2018. Contains 315270 sequences. (Running on oeis4.)