A367173 a(n) = the maximum number of distinct tilings of a polyomino of size n using any combination of polyomino tiles of sizes 1 through n.

1, 2, 4, 12, 24, 74, 148, 456, 1434, 2868, 8832, 27780

Offset

1,2

Comments

The sequence considers reflections and rotations as distinct tilings.

The polyominoes being tiled and the tiles themselves may be with or without holes.

The number of tilings of a 2-by-n rectangle is 2*A005668(n). Along with the fact that a(n+1) >= 2*a(n), because any added cell can either remain a monomino, or be joined to a neighboring polyomino, this yields a(1) through a(8). Other shapes take over beginning at a(9). - Charlie Neder, Sep 10 2025

Links

Table of n, a(n) for n=1..12.

Example

a(3) = 4 because any tromino can be tiled by (1) a tromino, (2) 3 monominoes, and (3) a monomino and a domino in two distinct ways.

Crossrefs

Cf. A000105, A367172, A367174.

Sequence in context: A129643 A332644 A200337 * A367703 A320931 A096421

Adjacent sequences: A367170 A367171 A367172 * A367174 A367175 A367176

Keyword

nonn,more

Author

John Mason from an idea of Craig Knecht, Nov 07 2023

Status

approved