A090632 - OEIS

%I #25 Aug 15 2017 03:16:03

%S 1,2,3,5,7,9,12,15,18,22,26,30,36,42,48,56,64,72,82,92,102,114,126,

%T 138,153,168,183,201,219,237,258,279,300,324,348,372,400,428,456,488,

%U 520,552,588,624,660,700,740,780,826,872,918,970,1022,1074,1132,1190,1248

%N 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.

%H Amanda Folsom et al, <a href="http://dx.doi.org/10.1016/j.disc.2015.12.019">On a general class of non-squashing partitions</a>, Discrete Mathematics 339.5 (2016): 1482-1506.

%H Youkow Homma, Jun Hwan Ryu and Benjamin Tong, <a href="http://sumry.yale.edu/sites/default/files/files/Sequence_nonsquashing_partitions.pdf">Sequence non-squashing partitions</a>, Slides from a talk, Jul 24 2014.

%H 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.

%H N. J. A. Sloane and J. A. Sellers, <a href="https://doi.org/10.1016/j.disc.2004.11.014">On non-squashing partitions</a>, Discrete Math., 294 (2005), 259-274.

%F 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)

%p 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

%Y Cf. A089054, A090631.

%Y Bisection of A064986.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Dec 13 2003

%E More terms from _Vladeta Jovovic_, May 22 2005

%E Further terms from _James A. Sellers_, Dec 23 2005