A323524 - OEIS

%I #11 Jan 21 2019 05:50:18

%S 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,

%T 1,35,43,9,6,124,1,10,77,158,1,110,1,285,186,12,1,742,2,170,203,1110,

%U 1,285,480,2115,306,15,1

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

%F a(p) = 1 and a(p^2) = 2 for p prime (see comment in A323349). - _Chai Wah Wu_, Jan 20 2019

%e 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:

%e   [1 1 2]

%e   [2 1 1]

%e   [1 2 1]

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

%K nonn,more

%O 0,5

%A _Gus Wiseman_, Jan 17 2019

%E a(16)-a(59) from _Chai Wah Wu_, Jan 20 2019