A385240 Array read by descending antidiagonals: T(n,k) is the number of k element sets of noncongruent integer sided rectangles that fill an n X n square.

1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 0, 0, 0, 3, 2, 1, 0, 0, 0, 3, 8, 2, 1, 0, 0, 0, 2, 15, 11, 3, 1, 0, 0, 0, 0, 19, 35, 19, 3, 1, 0, 0, 0, 0, 7, 87, 75, 23, 4, 1, 0, 0, 0, 0, 1, 114, 257, 119, 35, 4, 1, 0, 0, 0, 0, 0, 56, 593, 571, 210, 40, 5, 1, 0

Offset: 1

Author

Janaka Rodrigo, Aug 26 2025

Keywords

• nonn
• tabl
• new

Examples

			Array begins:
  1     0     0     0     0
  1     0     0     0     0
  1     1     2     0     0
  1     1     3     3     2
  1     2     8    15    19
  1     2    11    35    87
  1     3    19    75   257
  1     3    23   119   571
  1     4    35   210  1186
  1     4    40   289  2033
		

Crossrefs

Columns: A000012 (k=1), A004526 (k=2), A381847 (k=3), A387171 (k=4), A387241 (k=5).

Cf. A386296 (3-dimensional version).

Formula

T(n,1) = 1.

T(n,k) = 0 for k > n^2.

Extensions

More terms from Sean A. Irvine, Sep 02 2025