OFFSET
0,2
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.
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 A. Sellers and Vladeta Jovovic, May 26 2005 (corrected May 31 2005)
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 A. Sellers, Dec 23 2005
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 13 2003
EXTENSIONS
More terms from Vladeta Jovovic, May 22 2005
Further terms from James A. Sellers, Dec 23 2005
STATUS
approved