OFFSET
0,3
COMMENTS
Also the number of non-normal semi-magic rectangles summing to n with no zeros.
Matrices must be of size m X k where m, k are divisors of n and mk <= n. This implies that a(p) = 3 for p prime, since the only allowable matrices must be of size 1 X 1, 1 X p or p X 1 with only one way to fill in the entries for each matrix size. Similarly, a(p^2) = 6 with additional allowable matrices of sizes 1 X p^2, p^2 X 1 and p X p, again with only one way to fill in the entries for each size. - Chai Wah Wu, Jan 13 2019
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..59
FORMULA
a(p) = 3 and a(p^2) = 6 for p prime (see comment). - Chai Wah Wu, Jan 13 2019
EXAMPLE
The a(6) = 11 matrices:
[6] [3 3] [2 2 2] [1 1 1 1 1 1]
.
[3] [1 2] [2 1] [1 1 1]
[3] [2 1] [1 2] [1 1 1]
.
[2] [1 1]
[2] [1 1]
[2] [1 1]
.
[1]
[1]
[1]
[1]
[1]
[1]
MATHEMATICA
Table[Length[Select[Join@@Table[Partition[cmp, d], {cmp, Join@@Permutations/@IntegerPartitions[n]}, {d, Divisors[Length[cmp]]}], And[SameQ@@Total/@#, SameQ@@Total/@Transpose[#]]&]], {n, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 13 2019
EXTENSIONS
a(21)-a(31) from Chai Wah Wu, Jan 13 2019
a(32)-a(53) from Chai Wah Wu, Jan 14 2019
a(54) from Chai Wah Wu, Jan 16 2019
STATUS
approved