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A206440
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Volume of the last section of the set of partitions of n from the shell model of partitions version "Boxes".
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5
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1, 5, 11, 27, 43, 93, 131, 247, 352, 584, 808, 1306, 1735, 2643, 3568, 5160, 6835, 9721, 12672, 17564, 22832, 30818, 39743, 53027, 67594, 88740, 112752, 145944, 183979, 236059, 295370, 375208, 467363, 588007, 728437, 910339, 1121009, 1391083, 1706003, 2103013
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OFFSET
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1,2
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COMMENTS
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Since partial sums of this sequence give A066183 we have that A066183(n) is also the volume of the mentioned version of the shell model of partitions with n shells. Each part of size k has a volume equal to k^2 since each box is a cuboid whose sides have lengths: 1, k, k.
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LINKS
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, n],
b(n, i-1)+(p-> p+[0, p[1]*i^2])(b(n-i, min(n-i, i))))
end:
a:= n-> (b(n$2)-b(n-1$2))[2]:
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n == 0 || i == 1, {1, n},
b[n, i-1] + Function[p, p + {0, p[[1]]*i^2}][b[n-i, Min[n-i, i]]]];
a[n_] := (b[n, n] - b[n-1, n-1])[[2]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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