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

Author

N. J. A. Sloane, Dec 13 2003

Keywords

• nonn

Examples

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

Links

• 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.

Crossrefs

Cf. A089054, A090632.

Programs

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 Sellers, Dec 23 2005

Formula

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

Extensions

More terms from James Sellers, Dec 23 2005