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A370723
Number of symmetric (0,1)-matrices with sum of entries equal to n and no zero rows or columns, with weakly decreasing row sums and column sums.
0
1, 2, 5, 14, 39, 123, 393, 1352, 4782, 17824, 68481, 274166
OFFSET
1,2
EXAMPLE
The a(3) = 5 matrices:
[1 0 0] [1 0 0] [0 1 0] [0 0 1] [1 1]
[0 1 0] [0 0 1] [1 0 0] [0 1 0] [1 0]
[0 0 1] [0 1 0] [0 0 1] [1 0 0]
MATHEMATICA
a[0] = 1;
a[n_] := a[n] = Length[Select[Subsets[Tuples[Range[n], 2], {n}], Module[{matrix, rows, cols}, matrix = ConstantArray[0, {n, n}]; (matrix[[#[[1]], #[[2]]]] = 1) & /@ #; rows = Total[matrix, {2}]; cols = Total[matrix, {1}]; And[Union[First /@ #] == Range[Max @@ First /@ #], Union[Last /@ #] == Range[Max @@ Last /@ #], Sort[Reverse /@ #] == #, OrderedQ[Reverse[rows]], OrderedQ[Reverse[cols]]]] &]];
Table[a[n], {n, 1, 6}] (* Robert P. P. McKone, May 19 2024, from Gus Wiseman in A135588 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Ludovic Schwob, May 18 2024
STATUS
approved