A090631 Given n boxes labeled 1..n, such that box i weighs 2i 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, 4, 6, 9, 12, 17, 22, 29, 36, 45, 54, 66, 78, 93, 108, 126, 144, 167, 190, 218, 246, 279, 312, 352, 392, 439, 486, 540, 594, 657, 720, 792, 864, 945, 1026, 1119, 1212, 1317, 1422, 1539, 1656, 1788, 1920, 2067, 2214, 2376, 2538, 2718, 2898, 3096, 3294

Offset

0,2

Links

Table of n, a(n) for n=0..51.

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

G.f.: 1/(1-q)^2/Product_{i>=0} (1 - q^(2*3^i)). - James A. Sellers, Dec 23 2005

Example

The a(4) = 9 possible stacks are: empty, 1, 2, 3, 4, 12, 13, 14, 24.

Maple

p:=1/(1-q)^2/product((1-q^(2*3^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

Cf. A089054, A090632.

Sequence in context: A229093 A342371 A064985 * A001365 A102379 A238374

Adjacent sequences: A090628 A090629 A090630 * A090632 A090633 A090634

Keyword

nonn

Author

N. J. A. Sloane, Dec 13 2003

Extensions

More terms from James A. Sellers, Dec 23 2005

Status

approved