A321446
Number of (0,1)-matrices with n ones, no zero rows or columns, and distinct rows and columns.
Original entry on oeis.org
1, 1, 2, 10, 72, 624, 6522, 80178, 1129368, 17917032, 316108752, 6138887616, 130120838400, 2989026225696, 73964789192400, 1961487062520720, 55495429438186920, 1668498596700706440, 53122020640948010640, 1785467619718933936560, 63175132023953553400440
Offset: 0
The a(3) = 10 matrices:
[1 1] [1 1] [1 0] [0 1]
[1 0] [0 1] [1 1] [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]
Cf.
A000612,
A007716,
A049311,
A101370,
A120733,
A135589,
A283877,
A316980,
A319559,
A321515,
A321586,
A321587,
A321588,
A369285.
-
prs2mat[prs_]:=Table[Count[prs,{i,j}],{i,Union[First/@prs]},{j,Union[Last/@prs]}];
Table[Length[Select[Subsets[Tuples[Range[n],2],{n}],And[Union[First/@#]==Range[Max@@First/@#],Union[Last/@#]==Range[Max@@Last/@#],UnsameQ@@prs2mat[#],UnsameQ@@Transpose[prs2mat[#]]]&]],{n,6}]
-
\\ Q(m, n, wf) defined in A321588.
seq(n)={my(R=vectorv(n,m,Q(m,n,w->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
A321515
Number of nonnegative integer matrices with sum of entries equal to n, no zero rows or columns, and distinct rows and columns.
Original entry on oeis.org
1, 1, 3, 19, 137, 1209, 12899, 160395, 2276229, 36323217, 643848837, 12551081501, 266868756473, 6146455542737, 152439235077709, 4050427673024753, 114791270281213209, 3456412742412516649, 110191808168628510207, 3708004806262196242699, 131339701217968663631857
Offset: 0
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]
-
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}]
-
\\ 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
A369285
Number of connected binary matrices with n ones, no zero rows or columns, and distinct rows and columns.
Original entry on oeis.org
1, 1, 0, 4, 12, 72, 522, 4386, 42360, 465792, 5697552, 77229216, 1145762400, 18485254536, 322206163200, 6033964218720, 120830927523240, 2576515514434920, 58285369894027440, 1394212928447354640, 35160926971256369400, 932396530226753051160, 25936228654879236020640
Offset: 0
The a(3) = 4 matrices:
[1 1] [1 1] [1 0] [0 1]
[1 0] [0 1] [1 1] [1 1]
-
\\ Q, ConnectedMats defined in A321588.
seq(n)={my(R=vectorv(n,m,Q(m,n,w->1 + y^w + O(y*y^n)))); for(i=2, #R, R[i] -= i*R[i-1]); Vec(1 + vecsum(vecsum(Vec(ConnectedMats(Mat(R))))))}
Showing 1-3 of 3 results.