A090632 Given n boxes labeled 1..n, such that box i weighs 3i 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.
1, 2, 3, 5, 7, 9, 12, 15, 18, 22, 26, 30, 36, 42, 48, 56, 64, 72, 82, 92, 102, 114, 126, 138, 153, 168, 183, 201, 219, 237, 258, 279, 300, 324, 348, 372, 400, 428, 456, 488, 520, 552, 588, 624, 660, 700, 740, 780, 826, 872, 918, 970, 1022, 1074, 1132, 1190, 1248
Offset: 0
Keywords
Links
- Amanda Folsom et al, On a general class of non-squashing partitions, Discrete Mathematics 339.5 (2016): 1482-1506.
- Youkow Homma, Jun Hwan Ryu and Benjamin Tong, Sequence non-squashing partitions, Slides from a talk, Jul 24 2014.
- Oystein J. Rodseth, Sloane's box stacking problem, Discrete Math. 306 (2006), no. 16, 2005-2009.
- N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.
Programs
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Maple
p:=1/(1-q)^2/product((1-q^(3*4^i)), i=0..5): s:=series(p,q,100): for n from 0 to 99 do printf(`%d,`, coeff(s,q,n)) od: # James Sellers, Dec 23 2005
Formula
More generally, let a_k(n), k > 1, denote the number of stacks of boxes that can be formed such that no box is squashed wherein we have n boxes labeled 1..n such that box i weighs k*i grams and can support a total weight of i grams. Then a_k(n) has g.f. 1/((1-x)^2*Product_{i>=0} (1-x^(k*(k+1)^i))). - George Andrews, James Sellers and Vladeta Jovovic, May 26 2005 (corrected May 31 2005)
Extensions
More terms from Vladeta Jovovic, May 22 2005
Further terms from James Sellers, Dec 23 2005
Comments