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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 (list; graph; refs; listen; history; text; internal format)
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 partition-counting 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)^(n-k) * A279329(k).

a(n) + a(n-1) = 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(n-c, c+1))); (s)); }; \\ Antti Karttunen, Aug 30 2017

CROSSREFS

Cf. A003108, A078128, A279329.

Sequence in context: A217096 A267142 A185119 * A304002 A279760 A287457

Adjacent sequences:  A280127 A280128 A280129 * A280131 A280132 A280133

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 26 2016

STATUS

approved

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Last modified October 18 18:10 EDT 2018. Contains 316323 sequences. (Running on oeis4.)