OFFSET
1,7
COMMENTS
Also the number of nonnegative integer square matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, with row sums and column sums all equal to d.
A non-normal semi-magic square multiset partition of weight n is a multiset partition of weight n whose part sizes and vertex degrees are all equal to d, for some d|n.
The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..207 (rows 1..50)
Wikipedia, Magic square
FORMULA
T(n,d) = A333733(d, n/d). - Andrew Howroyd, Apr 11 2020
EXAMPLE
Triangle begins:
1
1 1
1 1
1 2 1
1 1
1 2 3 1
1 1
1 3 5 1
1 5 1
1 3 7 1
Inequivalent representatives of the a(10,5) = 7 semi-magic squares (zeros not shown):
[2 ] [2 ] [2 ] [2 ] [2 ] [11 ] [11 ]
[ 2 ] [ 2 ] [ 2 ] [ 11 ] [ 11 ] [11 ] [1 1 ]
[ 2 ] [ 2 ] [ 11 ] [ 11 ] [ 1 1 ] [ 11 ] [ 1 1 ]
[ 2 ] [ 11] [ 1 1] [ 11] [ 1 1] [ 1 1] [ 1 1]
[ 2] [ 11] [ 11] [ 11] [ 11] [ 11] [ 11]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Nov 18 2018
EXTENSIONS
a(28)-a(39) from Chai Wah Wu, Jan 16 2019
Terms a(40) and beyond from Andrew Howroyd, Apr 11 2020
STATUS
approved