A348454 Irregular triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n^2) is the number of ways to tile an n X n chessboard with rook-connected polyominoes of area k.

1, 1, 2, 0, 1, 1, 0, 10, 0, 0, 0, 0, 0, 1, 1, 36, 0, 117, 0, 0, 0, 70, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 4006, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6728, 80092, 178939, 0, 451206, 0, 0, 442791, 0, 0, 264500, 0, 0, 0, 0, 0, 80518, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 158753814, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Author

N. J. A. Sloane, Oct 27 2021

Keywords

• nonn
• tabf

Comments

This is an essentially identical triangle to A348452, except that the data in each row has effectively been reversed. Rather than copying everything here, please refer to A348452 for further information.

Examples

			Triangle begins:
1,
1, 2, 0, 1,
1, 0, 10, 0, 0, 0, 0, 0, 1,
1, 36, 0, 117, 0, 0, 0, 70, 0, 0, 0, 0, 0, 0, 0, 1,
1, 0, 0, 0, 4006, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
1, 6728, 80092, 178939, 0, 451206, 0, 0, 442791, 0, 0, 264500, 0, 0, 0, 0, 0, 80518, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
1, 0, 0, 0, 0, 0, 158753814, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
...
		

Crossrefs

Cf. A348452, A348453, A348455, and A348456.

Extensions

More than the usual number of terms are given, in order to show the first seven rows.