A335547 a(n) is the number of ways to tile a size n staircase polyomino with staircase polyominoes in the same direction as the size n staircase polyomino.

1, 2, 5, 18, 94, 709, 7710, 120882, 2732104, 89015152, 4180822859, 283067837700, 27628050712667, 3887236104777699, 788428930992492718, 230523466443694083587, 97162501670167108808501, 59035492675117768533460333, 51708108674446390274283614578, 65288256486029805607741923173692

Offset: 1

Author

Seiichi Manyama, Sep 12 2020

Keywords

• nonn

Comments

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

Examples

			For n = 3 the a(3) = 5 tilings are:
+---+          +---+          +---+          +---+
|   |          |   |          |   |          |   |
+---+---+      +   +---+      +---+---+      +---+---+
|   |   |      |       |      |   |   |      |   |   |
+---+---+---+, +---+---+---+, +   +---+---+, +---+   +---+,
|   |   |   |  |   |   |   |  |       |   |  |   |       |
+---+---+---+  +---+---+---+  +---+---+---+  +---+---+---+
+---+
|   |
+   +---+
|       |
+       +---+.
|           |
+---+---+---+
For n = 4 the a(4) = 5+5+3+3+2 = 18 tilings are:
+---+              +---+              +---+
|   |              |   |              |   |
+---+---+          +---+---+          +---+---+
|   |   |          |   |   |          |   |   |
+---+---+---+      +---+---+---+      +---+---+---+
|   |   |   |      |   |   |   |      |   |   |   |
+---+---+---+---+, +   +---+---+---+, +---+   +---+---+,
|   |   |   |   |  |       |   |   |  |   |       |   |
+---+---+---+---+  +---+---+---+---+  +---+---+---+---+
+---+              +---+              +---+
|   |              |   |              |   |
+---+---+          +---+---+          +   +---+
|   |   |          |   |   |          |       |
+---+---+---+      +---+---+---+      +---+---+---+
|   |   |   |      |   |   |   |      |   |   |   |
+---+---+   +---+, +   +---+   +---+, +---+---+---+---+,
|   |   |       |  |       |       |  |   |   |   |   |
+---+---+---+---+  +---+---+---+---+  +---+---+---+---+
+---+              +---+              +---+
|   |              |   |              |   |
+   +---+          +   +---+          +   +---+
|       |          |       |          |       |
+---+---+---+      +---+---+---+      +---+---+---+
|   |   |   |      |   |   |   |      |   |   |   |
+   +---+---+---+, +---+   +---+---+, +---+---+   +---+,
|       |   |   |  |   |       |   |  |   |   |       |
+---+---+---+---+  +---+---+---+---+  +---+---+---+---+
+---+              +---+              +---+
|   |              |   |              |   |
+   +---+          +---+---+          +---+---+
|       |          |   |   |          |   |   |
+---+---+---+      +   +---+---+      +   +---+---+
|   |   |   |      |       |   |      |       |   |
+   +---+   +---+, +---+---+---+---+, +       +---+---+,
|       |       |  |   |   |   |   |  |           |   |
+---+---+---+---+  +---+---+---+---+  +---+---+---+---+
+---+              +---+              +---+
|   |              |   |              |   |
+---+---+          +---+---+          +---+---+
|   |   |          |   |   |          |   |   |
+   +---+---+      +---+   +---+      +---+   +---+
|       |   |      |   |       |      |   |       |
+---+---+   +---+, +---+---+---+---+, +   +---+---+---+,
|   |   |       |  |   |   |   |   |  |       |   |   |
+---+---+---+---+  +---+---+---+---+  +---+---+---+---+
+---+              +---+              +---+
|   |              |   |              |   |
+---+---+          +   +---+          +   +---+
|   |   |          |       |          |       |
+---+   +---+      +       +---+      +       +---+
|   |       |      |           |      |           |
+---+       +---+, +---+---+---+---+, +           +---+.
|   |           |  |   |   |   |   |  |               |
+---+---+---+---+  +---+---+---+---+  +---+---+---+---+
a(5) = 8+5+5+5+3+8+5+5+5+3+8+3+5+8+5+3+8+2 = 94.
		

Links

• Code Golf Stack Exchange user "Bubbler", Tiling a staircase with staircases.
• Rémy Sigrist, PARI program for A335547

Crossrefs

Cf. A334617, A335967, A336479.

Programs

PARI

See Links section.

Extensions

More terms from Rémy Sigrist, Sep 13 2020