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

0,1

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

Table of n, a(n) for n=0..44.

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.

Formula

See A089054 for g.f.

Crossrefs

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

Sequence in context: A104899 A057975 A260881 * A305122 A276677 A112128

Adjacent sequences: A089052 A089053 A089054 * A089056 A089057 A089058

Keyword

nonn

Author

N. J. A. Sloane, Dec 04 2003

Status

approved