A303942 Number of partitions of n into at most 1 copy of 1^2, 2 copies of 2^2, 3 copies of 3^2, ... .

1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 1, 0, 1, 2, 2, 1, 1, 1, 1, 1, 1, 3, 3, 2, 1, 2, 2, 1, 2, 3, 4, 3, 3, 2, 2, 2, 2, 4, 4, 4, 3, 4, 3, 2, 3, 5, 7, 5, 5, 5, 6, 4, 3, 6, 8, 8, 5, 6, 6, 6, 6, 7, 9, 9, 10, 8, 8, 7, 8, 10, 11, 12, 10, 11, 10, 10, 9, 12, 15, 14, 14

Offset

0,10

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

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

Example

   n |              | a(n)
-----+--------------+------
   1 | 1            |  1
   4 | 4            |  1
   5 | 4+1          |  1
   8 | 4+4          |  1
   9 | 9, 4+4+1     |  2
  10 | 9+1          |  1
  13 | 9+4          |  1
  14 | 9+4+1        |  1
  16 | 16           |  1
  17 | 16+1, 9+4+4  |  2
  18 | 9+9, 9+4+4+1 |  2

Crossrefs

Cf. A011379, A033461, A052335, A303944, A303947.

Sequence in context: A304096 A151692 A280829 * A321928 A321917 A115201

Adjacent sequences: A303939 A303940 A303941 * A303943 A303944 A303945

Keyword

nonn,look

Author

Seiichi Manyama, May 03 2018

Status

approved