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A321653 Number of nonnegative integer matrices with sum of entries equal to n and no zero rows or columns, with strictly decreasing row sums and column sums. 9
1, 1, 1, 5, 5, 14, 44, 72, 147, 381, 1405 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..10.

EXAMPLE

The a(5) = 14 matrices:

  [5] [4 1] [3 2]

.

  [4] [4 0] [3 1] [3 1] [3] [3 0] [3 0] [2 2] [2 1] [2 1] [1 2]

  [1] [0 1] [1 0] [0 1] [2] [1 1] [0 2] [1 0] [2 0] [1 1] [2 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/@#]==Range[Max@@Last/@#], OrderedQ[Total/@prs2mat[#], Greater], OrderedQ[Total/@Transpose[prs2mat[#]], Greater]]&]], {n, 6}]

CROSSREFS

Cf. A000219, A001970, A007716, A068313, A114736, A117433, A120733, A319646, A321645, A321652, A321654, A321655.

Sequence in context: A317617 A294750 A304300 * A247940 A061200 A255304

Adjacent sequences:  A321650 A321651 A321652 * A321654 A321655 A321656

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 15 2018

STATUS

approved

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Last modified August 3 20:08 EDT 2020. Contains 336201 sequences. (Running on oeis4.)