The On-Line Encyclopedia of Integer Sequences (OEIS)

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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.
(history; published version)

#15 by Joerg Arndt at Tue Aug 15 03:15:57 EDT 2017

STATUS

proposed

approved

#14 by Michel Marcus at Tue Aug 15 02:31:29 EDT 2017

STATUS

editing

proposed

#13 by Michel Marcus at Tue Aug 15 02:31:23 EDT 2017

REFERENCES

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

LINKS

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.

#12 by Michel Marcus at Tue Aug 15 02:29:53 EDT 2017

LINKS

N. J. A. Sloane and J. A. Sellers, <a href="httphttps://arXivdoi.org/abs/math10.CO1016/0312418j.disc.2004.11.014">On non-squashing partitions</a>, Discrete Math., 294 (2005), 259-274.

STATUS

proposed

editing

#11 by Jon E. Schoenfield at Tue Aug 15 01:34:18 EDT 2017

STATUS

editing

proposed

#10 by Jon E. Schoenfield at Tue Aug 15 01:34:15 EDT 2017

FORMULA

Generating functionG.f.: 1/(1-q)^2/product(Product_{i>=0} (1 - q^(2*3^i)), i=0..infinity) - James A. Sellers, Dec 23 2005

EXAMPLE

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

MAPLE

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

STATUS

approved

editing

#9 by Russ Cox at Sat Mar 31 10:30:33 EDT 2012

FORMULA

Generating function: 1/(1-q)^2/product((1-q^(2*3^i)), i=0..infinity) - _James A. Sellers (sellersj(AT)math.psu.edu), _, Dec 23 2005

EXTENSIONS

More terms from _James A. Sellers (sellersj(AT)math.psu.edu), _, Dec 23 2005

Discussion

Sat Mar 31

10:30

OEIS Server: https://oeis.org/edit/global/639

#8 by Russ Cox at Fri Mar 30 16:49:51 EDT 2012

AUTHOR

_N. J. A. Sloane (njas(AT)research.att.com), _, Dec 13 2003

Discussion

Fri Mar 30

16:49

OEIS Server: https://oeis.org/edit/global/110

#7 by N. J. A. Sloane at Sun Dec 04 01:00:45 EST 2011

STATUS

editing

approved

#6 by N. J. A. Sloane at Sun Dec 04 01:00:42 EST 2011

REFERENCES

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

STATUS

approved

editing