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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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)