A334617 a(n) is the number of ways to tile a size n staircase polyomino with staircase polyominoes.

1, 2, 8, 57, 806, 20840, 1038266, 97115638, 17213517207, 5768580741287

Offset: 1

Author

Peter Kagey, Sep 08 2020

Keywords

• nonn
• more

Comments

A size-n staircase polynomo is a polyomino consisting of n left-aligned rows in increasing length of 1, 2, ..., n. Rotations of staircase polyominoes are also polyominoes.

Examples

			For n = 3 the a(3) = 8 tilings are:
+---+          +---+          +---+          +---+
|   |          |   |          |   |          |   |
+---+---+      +   +---+      +---+---+      +---+---+
|   |   |      |       |      |   |   |      |   |   |
+---+---+---+, +---+---+---+, +   +---+---+, +---+   +---+,
|   |   |   |  |   |   |   |  |       |   |  |   |       |
+---+---+---+  +---+---+---+  +---+---+---+  +---+---+---+
+---+          +---+          +---+          +---+
|   |          |   |          |   |          |   |
+---+---+      +---+---+      +---+---+      +   +---+
|       |      |       |      |   |   |      |       |
+---+   +---+, +   +---+---+, +---+   +---+, +       +---+.
|   |   |   |  |   |   |   |  |       |   |  |           |
+---+---+---+  +---+---+---+  +---+---+---+  +---+---+---+
		

Links

• Code Golf Stack Exchange user "Bubbler", Tiling a staircase with staircases.

Crossrefs

Cf. A000105, A045846, A219924, A254414, A335547.

Extensions

a(8) from Seiichi Manyama, Sep 09 2020

a(9)-a(10) from Bert Dobbelaere, Sep 12 2020