

A280130


Expansion of Product_{k>=2} (1 + x^(k^3)).


5



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

0


COMMENTS

Number of partitions of n into distinct cubes > 1.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100000 (first 10001 terms from Antti Karttunen)
Index entries for sequences related to sums of cubes
Index entries for related partitioncounting sequences


FORMULA

G.f.: Product_{k>=2} (1 + x^(k^3)).
From Vaclav Kotesovec, Dec 26 2016: (Start)
a(n) = Sum_{k=0..n} (1)^(nk) * A279329(k).
a(n) + a(n1) = A279329(n).
a(n) ~ A279329(n)/2.
(End)


EXAMPLE

a(35) = 1 because we have [27, 8].
From Antti Karttunen, Aug 30 2017: (Start)
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 also the first point where the sequence obtains value larger than one. (End)


MATHEMATICA

nmax = 130; CoefficientList[Series[Product[1 + x^k^3, {k, 2, nmax}], {x, 0, nmax}], x]


PROG

(PARI) A280130(n, m=2) = { my(s=0); if(!n, 1, for(c=m, n, if(ispower(c, 3), s+=A280130(nc, c+1))); (s)); }; \\ Antti Karttunen, Aug 30 2017


CROSSREFS

Cf. A003108, A078128, A279329.
Sequence in context: A015494 A267142 A185119 * A304002 A126811 A014057
Adjacent sequences: A280127 A280128 A280129 * A280131 A280132 A280133


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Dec 26 2016


STATUS

approved



