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.

1, 2, 5, 14, 39, 123, 393, 1352, 4782, 17824, 68481, 274166

Offset

1,2

Links

Table of n, a(n) for n=1..12.

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

Cf. A178718, A135588, A321652, A365961.

Sequence in context: A339289 A003054 A317553 * A148316 A148317 A148318

Adjacent sequences: A370720 A370721 A370722 * A370724 A370725 A370726

Keyword

nonn,more

Author

Ludovic Schwob, May 18 2024

Status

approved