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A321732 Number of nonnegative integer square matrices with sum of entries equal to n, no zero rows or columns, and the same row sums as column sums. 5
1, 1, 3, 11, 53, 317, 2293 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..6.

EXAMPLE

The a(3) = 11 matrices:

  [3]

.

  [2 0] [1 1] [1 0] [0 1]

  [0 1] [1 0] [0 2] [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

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]}]];

Table[Length[Select[multsubs[Tuples[Range[n], 2], n], And[Union[First/@#]==Range[Max@@First/@#]==Union[Last/@#], Total/@prs2mat[#]==Total/@Transpose[prs2mat[#]]]&]], {n, 5}]

CROSSREFS

Cf. A000700, A000701, A006052, A007016, A120732, A319056, A320451, A321718, A321719, A321722, A321733, A321734, A321735, A321736, A321739.

Sequence in context: A000255 A318912 A121580 * A224345 A081367 A156171

Adjacent sequences:  A321729 A321730 A321731 * A321733 A321734 A321735

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 18 2018

STATUS

approved

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)