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A280130
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Expansion of Product_{k>=2} (1 + x^(k^3)).
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5
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1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1
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OFFSET
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0
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COMMENTS
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Number of partitions of n into distinct cubes > 1.
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LINKS
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FORMULA
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G.f.: Product_{k>=2} (1 + x^(k^3)).
a(n) = Sum_{k=0..n} (-1)^(n-k) * A279329(k).
(End)
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EXAMPLE
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a(35) = 1 because 35 = 27 + 8. This is the first nonzero value for a noncube index.
a(72) = 1 because there is just one solution: 72 = 4^3 + 2^3.
a(216) = 2 because there are two solutions: 216 = 6^3 = 5^3 + 4^3 + 3^3. This is the first index where a(n) > 1. (End)
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MATHEMATICA
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nmax = 130; CoefficientList[Series[Product[1 + x^k^3, {k, 2, nmax}], {x, 0, nmax}], x]
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PROG
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(PARI)
A280130(n, m=2)={if(n, sum(c=m, sqrtnint(n, 3), A280130(n-c^3, c+1)), 1)} \\ At n ~ 2500 this is about 100 times faster than code from 2017, but for larger n (needed for A030272(n)=a(n^3)) better use (with parisize (or allocmem) >= 201*Nmax):
V280130=Vecsmall(prod(k=2, (Nmax=3*10^4)^(1/3), 1+x^k^3+O(x^Nmax))); A280130(n)=V280130[n+1] \\ M. F. Hasler, Jan 05 2020
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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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