A303942 -id:A303942 - cp's OEIS frontend

A303947 Number of partitions of n into at most 1 copy of 2^2, 2 copies of 3^2, 3 copies of 4^2, ... .

1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 1, 2, 0, 1, 0, 3, 0, 1, 1, 2, 3, 0, 2, 1, 4, 0, 1, 2, 2, 2, 0, 4, 1, 2, 1, 3, 3, 1, 3, 1, 5, 1, 3, 2, 4, 3, 1, 4, 2, 4, 1, 5, 3, 3, 4, 4, 6, 2, 4

Offset: 0

Seiichi Manyama, May 03 2018

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

Cf. A033461, A087153, A303942.

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

A304021 Number of partitions of n into at most 1 copy of 1^3, 2 copies of 2^3, 3 copies of 3^3, ... .

Original entry on oeis.org

1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1

Offset: 0

Seiichi Manyama, May 04 2018

nonn

			   n |                    | a(n)
-----+--------------------+------
   1 | 1                  |  1
   8 | 8                  |  1
   9 | 8+1                |  1
  16 | 8+8                |  1
  17 | 8+8+1              |  1
  27 | 27                 |  1
  28 | 27+1               |  1
  35 | 27+8               |  1
  36 | 27+8+1             |  1
  43 | 27+8+8             |  1
  ...
  81 | 64+8+8+1, 27+27+27 |  2

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

Cf. A303942, A304002.

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

A303944 Number of partitions of n into at most 1^2 copy of 1, 2^2 copies of 2, 3^2 copies of 3, ... .

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 6, 8, 11, 15, 19, 25, 34, 43, 55, 71, 90, 113, 143, 178, 222, 276, 340, 418, 515, 628, 765, 931, 1128, 1362, 1643, 1974, 2369, 2836, 3385, 4033, 4800, 5694, 6745, 7978, 9418, 11096, 13057, 15334, 17985, 21062, 24626, 28753, 33534, 39045, 45408, 52744, 61187

Offset: 0

Seiichi Manyama, May 03 2018

nonn

			  n |                                | a(n)
----+--------------------------------+------
  1 | 1                              |  1
  2 | 2                              |  1
  3 | 3, 2+1                         |  2
  4 | 4, 3+1, 2+2                    |  3
  5 | 5, 4+1, 3+2, 2+2+1             |  4
  6 | 6, 5+1, 4+2, 3+3, 3+2+1, 2+2+2 |  6

Cf. A034262, A052335, A303942.

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

cp's OEIS Frontend

A303947 Number of partitions of n into at most 1 copy of 2^2, 2 copies of 3^2, 3 copies of 4^2, ... .

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A304021 Number of partitions of n into at most 1 copy of 1^3, 2 copies of 2^3, 3 copies of 3^3, ... .

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A303944 Number of partitions of n into at most 1^2 copy of 1, 2^2 copies of 2, 3^2 copies of 3, ... .

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