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Search: id:A090632
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| A090632 |
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Given n boxes labeled 1..n, such that box i weighs 3i 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, 3, 5, 7, 9, 12, 15, 18, 22, 26, 30, 36, 42, 48, 56, 64, 72, 82, 92, 102, 114, 126, 138, 153, 168, 183, 201, 219, 237, 258, 279, 300, 324, 348, 372, 400, 428, 456, 488, 520, 552, 588, 624, 660, 700, 740, 780, 826, 872, 918, 970, 1022, 1074, 1132, 1190, 1248
(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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More generally, let a_k(n), k>1, denote the number of stacks of boxes that can be formed such that no box is squashed wherein we have n boxes labeled 1..n such that box i weighs k*i grams and can support a total weight of i grams. Then a_k(n) has g.f. 1/((1-x)^2*Product_{i>=0} (1-x^(k*(k+1)^i))). - George Andrews, James Sellers and Vladeta Jovovic, May 26 2005 (corrected May 31 2005)
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MAPLE
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p:=1/(1-q)^2/product((1-q^(3*4^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, A090631.
Sequence in context: A022794 A025693 A117930 this_sequence A022786 A005704 A022782
Adjacent sequences: A090629 A090630 A090631 this_sequence A090633 A090634 A090635
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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 Vladeta Jovovic (vladeta(AT)Eunet.yu), May 22 2005
Further terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 2005
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