A067769 Number of tiling variants for polyominoes with n cells.

1, 2, 3, 10, 12, 43, 48, 171, 253, 632, 815, 3205, 3236, 9304, 17434, 39810, 48693, 162562, 185199, 595067, 892322

Offset

1,2

Comments

Considers only translations, and not rotations or reflections, of polyominoes without holes tallied in A000104(n) (polyominoes with holes, A001419, cannot tessellate), tiled to lattices tallied in A000203(n) (or A145393(n) allowing for rotations and reflections), reduced for overall symmetry. - Charles L. Hohn, Apr 23 2026

Links

Table of n, a(n) for n=1..21.

Charles L. Hohn, C++ program for generating terms, 2026.

A. V. Maleev, An Algorithm and Program of Exhaustive Search for Possible Tiling of a Plane with Polyominoes, Crystallography Reports, [abstract; translation of Krystallografiya], 46 (No. 1, 2001), 154-156.

Example

From Charles L. Hohn, Apr 23 2026: (Start)
a(4) = 10:
  +--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+  +    +--+--+--+  +
  |           |    |           |    |           |    |        |  |    |        |  |
  +--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +  +--+--+--+    +--+  +--+--+
  |           |       |                   |          |  |        |       |  |
  +--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+  +--+--+    +--+--+--+  +
  |           |          |          |           |       |  |          |        |  |
  +--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+  +--+    +--+  +--+--+
  |           |             |             |                |  |          |  |
  +--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+  +    +--+--+--+  +
  +--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+  +--+
  |     |     |    |     |     |    |     |     |    |     |     |    |     |     |
  +     +     +    +     +     +    +--+  +--+  +    +--+  +--+  +    +--+  +--+--+
  |     |     |    |     |     |       |     |          |     |          |     |
  +--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +  +--+--+--+
  |     |     |       |     |       |     |     |       |     |       |     |     |
  +     +     +       +     +       +--+  +--+  +    +  +--+  +--+    +--+--+--+  +
  |     |     |       |     |          |     |       |     |     |       |     |
  +--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+  +--+
(End)

Prog

(C++) // see Hohn link.

Crossrefs

Cf. A000104, A000203, A145393.

Sequence in context: A069124 A371810 A218028 * A066089 A203235 A256214

Adjacent sequences: A067766 A067767 A067768 * A067770 A067771 A067772

Keyword

nonn,more,hard

Author

N. J. A. Sloane, Feb 09 2002

Extensions

a(13)-a(21) from Charles L. Hohn, Apr 23 2026

Status

approved