A291806 The number of polyomino tilings of n X n square.

1, 5, 216, 212987, 2465119032, 283903861501885, 323106970416782690152, 3633528430503221551361684810, 403755321534856138801050834916449856, 443318134498373024791278075543353137772626440, 4809725522838960509505487707480206008562886812045111500, 515623439762296199132592853679608251140750035746786770609650972664

Offset

1,2

Comments

The sequence gives the number of distinct tilings by polyominoes of a square with side n. As for "free" polyominoes, tilings that are reflections or rotations of each other are not considered distinct.

Using the same terminology used for polyominoes: the corresponding sequence for "fixed" tilings is A145835, and the sequence for one-sided tilings begins 1, 5, 222, 213315.

Links

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

John Mason, Tiling examples.

John F. Rudge, Python program (github).

Crossrefs

Cf. A145835 (fixed), A268416 (polyominoes that will fit in n-sided square), A291807 (symmetric tilings), A291808 (tilings with distinct polyominoes), A291809 (tilings with differently sized polyominoes).

Sequence in context: A144796 A269823 A206457 * A119657 A235456 A159808

Adjacent sequences: A291803 A291804 A291805 * A291807 A291808 A291809

Keyword

nonn

Author

John Mason, Sep 01 2017

Extensions

a(5) from Christian Sievers, Feb 01 2026

a(6)-a(12) from John F. Rudge, Apr 05 2026

Status

approved