A323524 Number of integer partitions of n whose parts can be arranged into a square matrix with equal row and column sums.

1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 5, 1, 4, 4, 6, 1, 10, 1, 7, 10, 6, 1, 24, 2, 7, 22, 18, 1, 38, 1, 35, 43, 9, 6, 124, 1, 10, 77, 158, 1, 110, 1, 285, 186, 12, 1, 742, 2, 170, 203, 1110, 1, 285, 480, 2115, 306, 15, 1

Offset

0,5

Links

Table of n, a(n) for n=0..59.

Formula

a(p) = 1 and a(p^2) = 2 for p prime (see comment in A323349). - Chai Wah Wu, Jan 20 2019

Example

The a(12) = 5 integer partitions are (12), (5,5,1,1), (4,4,2,2), (3,3,3,3), (2,2,2,1,1,1,1,1,1). For example, such a matrix for (2,2,2,1,1,1,1,1,1) is:
  [1 1 2]
  [2 1 1]
  [1 2 1]

Crossrefs

Cf. A006052, A007016, A103198, A120732, A321719, A321722, A321725, A323306, A323347, A323349, A323523.

Sequence in context: A332267 A161148 A143773 * A354713 A265893 A191372

Adjacent sequences: A323521 A323522 A323523 * A323525 A323526 A323527

Keyword

nonn,more

Author

Gus Wiseman, Jan 17 2019

Extensions

a(16)-a(59) from Chai Wah Wu, Jan 20 2019

Status

approved