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

1,3

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.

Links

Table of n, a(n) for n=1..140.

Example

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.

Sequence in context: A075107 A269953 A326411 * A348452 A309163 A320655

Adjacent sequences: A348451 A348452 A348453 * A348455 A348456 A348457

Keyword

nonn,tabf

Author

N. J. A. Sloane, Oct 27 2021

Extensions

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

Status

approved