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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, 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
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]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jan 17 2019
EXTENSIONS
a(16)-a(59) from Chai Wah Wu, Jan 20 2019
STATUS
approved