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 A321588 Number of connected nonnegative integer matrices with sum of entries equal to n, no zero rows or columns, and distinct rows and columns. 2
 1, 1, 1, 9, 29, 181, 1285 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A matrix is connected if the positions in each row (or each column) of the nonzero entries form a connected hypergraph. LINKS EXAMPLE The a(4) = 29 matrices: 4 31 13 . 3 21 21 20 12 12 11 110 11 110 101 101 1 10 10 02 011 011 01 01 1 10 01 11 10 01 20 101 02 011 110 011 3 21 12 11 110 101 21 12 . 11 11 10 10 01 01 10 01 11 01 11 10 01 10 01 11 10 11 MATHEMATICA prs2mat[prs_]:=Table[Count[prs, {i, j}], {i, Union[First/@prs]}, {j, Union[Last/@prs]}]; multsubs[set_, k_]:=If[k==0, {{}}, Join@@Table[Prepend[#, set[[i]]]&/@multsubs[Drop[set, i-1], k-1], {i, Length[set]}]]; csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Union[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]]; 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[#]], Length[csm[Map[Last, GatherBy[#, First], {2}]]]==1]&]], {n, 6}] CROSSREFS Cf. A007718, A056156, A059201, A120733, A283877, A316980, A319557, A319558, A319559, A319565, A319647, A319616-A319629, A321446, A321515. Sequence in context: A146602 A146413 A146054 * A173262 A337445 A291159 Adjacent sequences: A321585 A321586 A321587 * A321589 A321590 A321591 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 13 2018 STATUS approved

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Last modified March 27 05:46 EDT 2023. Contains 361554 sequences. (Running on oeis4.)