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A321515
Number of nonnegative integer matrices with sum of entries equal to n, no zero rows or columns, and distinct rows and columns.
6
1, 1, 3, 19, 137, 1209, 12899, 160395, 2276229, 36323217, 643848837, 12551081501, 266868756473, 6146455542737, 152439235077709, 4050427673024753, 114791270281213209, 3456412742412516649, 110191808168628510207, 3708004806262196242699, 131339701217968663631857
OFFSET
0,3
LINKS
EXAMPLE
The a(3) = 19 matrices:
[3] [2 1] [1 2]
.
[2] [2 0] [1 1] [1 1] [1] [1 0] [1 0] [0 2] [0 1] [0 1]
[1] [0 1] [1 0] [0 1] [2] [1 1] [0 2] [1 0] [2 0] [1 1]
.
[1 0 0] [1 0 0] [0 1 0] [0 1 0] [0 0 1] [0 0 1]
[0 1 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [0 1 0]
[0 0 1] [0 1 0] [0 0 1] [1 0 0] [0 1 0] [1 0 0]
MATHEMATICA
multsubs[set_, k_]:=If[k==0, {{}}, Join@@Table[Prepend[#, set[[i]]]&/@multsubs[Drop[set, i-1], k-1], {i, Length[set]}]];
prs2mat[prs_]:=Table[Count[prs, {i, j}], {i, Union[First/@prs]}, {j, Union[Last/@prs]}];
Table[Length[Select[multsubs[Tuples[Range[n], 2], n], And[Union[First/@#]==Range[Max@@First/@#], Union[Last/@#]==Range[Max@@Last/@#], UnsameQ@@prs2mat[#], UnsameQ@@Transpose[prs2mat[#]]]&]], {n, 5}]
PROG
(PARI) \\ Q(m, n, wf) defined in A321588.
seq(n)={my(R=vectorv(n, m, Q(m, n, w->1/(1 - y^w) + O(y*y^n)))); for(i=2, #R, R[i] -= i*R[i-1]); Vec(1 + vecsum(vecsum(R)))} \\ Andrew Howroyd, Jan 24 2024
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 13 2018
EXTENSIONS
a(7) onwards from Andrew Howroyd, Jan 20 2024
STATUS
approved