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

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

0,4

Links

Table of n, a(n) for n=0..52.

Formula

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

Example

  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

Crossrefs

Cf. A034262, A052335, A303942.

Sequence in context: A262160 A132217 A265254 * A039855 A175868 A035950

Adjacent sequences: A303941 A303942 A303943 * A303945 A303946 A303947

Keyword

nonn

Author

Seiichi Manyama, May 03 2018

Status

approved