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A321733 Number of (0,1)-matrices with n ones, no zero rows or columns, and the same row sums as column sums. 3
1, 1, 2, 8, 40, 246, 1816, 15630, 153592, 1696760, 20816358, 280807868, 4131117440, 65823490088, 1129256780408 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..14.

EXAMPLE

The a(4) = 40 matrices:

  [1 1]

  [1 1]

.

  [1 1 0][1 1 0][1 0 1][1 0 1][1 0 0]

  [1 0 0][0 0 1][1 0 0][0 1 0][0 1 1]

  [0 0 1][1 0 0][0 1 0][1 0 0][0 1 0]

.

  [1 0 0][0 1 1][0 1 0][0 1 0][0 1 0]

  [0 0 1][1 0 0][1 1 0][1 0 1][0 1 1]

  [0 1 1][1 0 0][0 0 1][0 1 0][1 0 0]

.

  [0 1 0][0 0 1][0 0 1][0 0 1][0 0 1]

  [0 0 1][1 1 0][1 0 0][0 1 0][0 0 1]

  [1 0 1][0 1 0][0 1 1][1 0 1][1 1 0]

.

  [1 0 0 0][1 0 0 0][1 0 0 0][1 0 0 0][1 0 0 0][1 0 0 0]

  [0 1 0 0][0 1 0 0][0 0 1 0][0 0 1 0][0 0 0 1][0 0 0 1]

  [0 0 1 0][0 0 0 1][0 1 0 0][0 0 0 1][0 1 0 0][0 0 1 0]

  [0 0 0 1][0 0 1 0][0 0 0 1][0 1 0 0][0 0 1 0][0 1 0 0]

.

  [0 1 0 0][0 1 0 0][0 1 0 0][0 1 0 0][0 1 0 0][0 1 0 0]

  [1 0 0 0][1 0 0 0][0 0 1 0][0 0 1 0][0 0 0 1][0 0 0 1]

  [0 0 1 0][0 0 0 1][1 0 0 0][0 0 0 1][1 0 0 0][0 0 1 0]

  [0 0 0 1][0 0 1 0][0 0 0 1][1 0 0 0][0 0 1 0][1 0 0 0

.

  [0 0 1 0][0 0 1 0][0 0 1 0][0 0 1 0][0 0 1 0][0 0 1 0]

  [1 0 0 0][1 0 0 0][0 1 0 0][0 1 0 0][0 0 0 1][0 0 0 1]

  [0 1 0 0][0 0 0 1][1 0 0 0][0 0 0 1][1 0 0 0][0 1 0 0]

  [0 0 0 1][0 1 0 0][0 0 0 1][1 0 0 0][0 1 0 0][1 0 0 0]

.

  [0 0 0 1][0 0 0 1][0 0 0 1][0 0 0 1][0 0 0 1][0 0 0 1]

  [1 0 0 0][1 0 0 0][0 1 0 0][0 1 0 0][0 0 1 0][0 0 1 0]

  [0 1 0 0][0 0 1 0][1 0 0 0][0 0 1 0][1 0 0 0][0 1 0 0]

  [0 0 1 0][0 1 0 0][0 0 1 0][1 0 0 0][0 1 0 0][1 0 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[Subsets[Tuples[Range[n], 2], {n}], And[Union[First/@#]==Range[Max@@First/@#]==Union[Last/@#], Total/@prs2mat[#]==Total/@Transpose[prs2mat[#]]]&]], {n, 5}]

CROSSREFS

Cf. A006052, A007016, A049311, A054976, A057151, A104602, A120732, A319056, A321717, A321723, A321732, A321735, A321736, A321739.

Sequence in context: A319949 A304070 A259869 * A000828 A296676 A281910

Adjacent sequences:  A321730 A321731 A321732 * A321734 A321735 A321736

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 18 2018

EXTENSIONS

a(7)-a(14) from Lars Blomberg, May 23 2019

STATUS

approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)