A089055 Solution to the non-squashing boxes problem (version 2).

2, 4, 8, 16, 28, 46, 72, 108, 156, 218, 298, 398, 524, 678, 868, 1096, 1372, 1698, 2086, 2538, 3070, 3684, 4398, 5214, 6156, 7226, 8450, 9830, 11400, 13162, 15152, 17372, 19868, 22642, 25742, 29170, 32986, 37192, 41850, 46962, 52606, 58784, 65576, 72984, 81106

Offset: 0

Author

N. J. A. Sloane, Dec 04 2003

Keywords

• nonn

Comments

Given n+1 boxes labeled 0..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.

Links

• Amanda Folsom, Youkow Homma, Jun Hwan Ryu, and Benjamin Tong, On a general class of non-squashing partitions, Discrete Mathematics 339 (2016) 1482-1506.
• N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, arXiv:math/0312418 [math.CO], 2003; Discrete Math., 294 (2005), 259-274.

Crossrefs

Cf. A000123, A088567. Equals 2*A089054. Row sums of A089239.

Formula

See A089054 for g.f.