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A298934
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Number of partitions of n^2 into distinct cubes.
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4
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1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 3, 1, 0, 0, 0, 0, 0, 0, 3, 3, 1, 0, 3, 0, 2, 4, 0, 0, 1, 0, 0, 2, 3, 1, 1, 0, 6, 3, 6, 1, 6, 0, 3, 9, 0, 6, 6, 7, 0, 10, 3, 3, 6, 0, 8, 6, 13, 2, 10, 9, 10, 19, 2, 14, 21, 7, 2, 25
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OFFSET
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0,16
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LINKS
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FORMULA
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a(n) = [x^(n^2)] Product_{k>=1} (1 + x^(k^3)).
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EXAMPLE
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a(15) = 2 because we have [216, 8, 1] and [125, 64, 27, 8, 1].
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(n>i^2*(i+1)^2/4, 0, b(n, i-1)+
`if`(i^3>n, 0, b(n-i^3, i-1))))
end:
a:= n-> b(n^2, n):
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MATHEMATICA
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Table[SeriesCoefficient[Product[1 + x^k^3, {k, 1, Floor[n^(2/3) + 1]}], {x, 0, n^2}], {n, 0, 84}]
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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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