

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.


3



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
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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, 20052009.
N. J. A. Sloane and J. A. Sellers, On nonsquashing partitions, Discrete Math., 294 (2005), 259274.


FORMULA

G.f.: 1/(1q)^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/(1q)^2/product((1q^(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: A080556 A229093 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



