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Search: id:A090631
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| A090631 |
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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. |
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4
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| 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; listen)
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OFFSET
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0,2
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LINKS
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N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.
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FORMULA
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Generating function: 1/(1-q)^2/product((1-q^(2*3^i)), i=0..infinity) - James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 2005
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EXAMPLE
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For n=4 the a(4) = 9 possible stacks are: empty, 1, 2, 3, 4, 12, 13, 14, 24.
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MAPLE
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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: (Sellers)
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CROSSREFS
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Cf. A089054, A090632.
Sequence in context: A080548 A080556 A064985 this_sequence A001365 A102379 A133041
Adjacent sequences: A090628 A090629 A090630 this_sequence A090632 A090633 A090634
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KEYWORD
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nonn
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AUTHOR
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njas, Dec 13 2003
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 2005
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