A304002 Number of partitions of n into at most 1 copy of 2^3, 2 copies of 3^3, 3 copies of 4^3, ... .

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, 1, 0, 0, 0, 0, 0, 0, 0, 1, 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, 0

Offset

0

Links

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Formula

G.f.: Product_{k>=2} (1-x^(k^4))/(1-x^(k^3)).

Example

    n |                | a(n)
------+----------------+------
    8 | 8              |  1
   27 | 27             |  1
   35 | 27+8           |  1
   54 | 27+27          |  1
   62 | 27+27+8        |  1
   64 | 64             |  1
   72 | 64+8           |  1
   91 | 64+27          |  1
   99 | 64+27+8        |  1
  ...
  216 | 216, 125+64+27 |  2

Crossrefs

Cf. A087153, A303947, A304021.

Sequence in context: A373838 A185119 A280130 * A126811 A014057 A015689

Adjacent sequences: A303999 A304000 A304001 * A304003 A304004 A304005

Keyword

nonn

Author

Seiichi Manyama, May 04 2018

Status

approved