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A307609 Number of partitions of n^3 into consecutive positive cubes. 2
1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16861

Index entries for sequences related to sums of cubes

FORMULA

a(n) = [x^(n^3)] Sum_{i>=1} Sum_{j>=i} Product_{k=i..j} x^(k^3).

a(n) = A297199(A000578(n)).

a(n) >= 2 for n in A097811.

EXAMPLE

20^3 = 11^3 + 12^3 + 13^3 + 14^3, so a(20) = 2.

2856^3 = 213^3 +...+ 555^3 = 273^3 +...+ 560^3, so a(2856) = 3. See also Donovan Johnson's comment in A097811. - Antti Karttunen, Aug 22 2019

PROG

(PARI)

A297199(n) = { my(s=0, k=1, c); while((c=k^3) <= n, my(u=n-c, i=k); while(u>0, i++; c = i^3; u=u-c); s += (!u); k++); (s); };

A307609(n) = A297199(n^3); \\ Antti Karttunen, Aug 22 2019

CROSSREFS

Cf. A000578, A030272, A097811, A131643, A217843, A259792, A297199.

Sequence in context: A043288 A057523 A083235 * A043287 A212177 A249622

Adjacent sequences:  A307606 A307607 A307608 * A307610 A307611 A307612

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 18 2019

STATUS

approved

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Last modified August 12 02:46 EDT 2020. Contains 336436 sequences. (Running on oeis4.)