A307609 Number of partitions of n^3 into consecutive positive cubes.

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

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: A353786 A057523 A083235 * A043287 A212177 A345999

Adjacent sequences: A307606 A307607 A307608 * A307610 A307611 A307612

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 18 2019

Status

approved