A390142 The number of tiles composed of n equilateral squares and triangles.

1, 2, 3, 9, 41, 211, 1297, 8401, 56661, 389544

Offset

0,2

Comments

Tiles are sets of connected, non-overlapping equilateral squares and triangles. Tiles obtained by rotations, translations, and reflections are counted only once.

From Rhys Feltman, Apr 19 2026: (Start)

The following table gives the number of tiles having k squares for each size n:

k\n| 0 1 2 3 4 5 6 7 8 9

---+------------------------------------

0 | 1 1 1 1 3 4 12 24 66 160

1 | 1 1 3 7 24 71 232 726 2306

2 | 1 3 15 55 229 874 3366 12416

3 | 2 11 73 385 1914 8728 38220

4 | 5 43 388 2544 14779 77265

5 | 12 177 1968 15710 105054

6 | 35 737 9856 92136

7 | 108 3061 47995

8 | 369 12707

9 | 1285

Column totals are this sequence; leading diagonal is A000105; top line is A000577; n = 2k line is A395105. (End)

Links

Table of n, a(n) for n=0..9.

Rhys Feltman, Polyiamondominoes.

Kadon Enterprises, TRI-CHEX.

R. J. Mathar, C++ source code and Illustrations for small n zenodo:18499397 (2026).

Livio Zucca, Puzzle fun, facebook 2024 (restricted access).

Crossrefs

Cf. A000105, A000577, A390999, A395105.

Sequence in context: A125052 A181139 A162093 * A052828 A214915 A219673

Adjacent sequences: A390139 A390140 A390141 * A390143 A390144 A390145

Keyword

nonn,more

Author

R. J. Mathar, Jan 25 2026

Extensions

a(5), a(6) corrected. - R. J. Mathar, Jan 29 2026

a(7) corrected. - R. J. Mathar, Feb 05 2026

a(8) from Rhys Feltman, Apr 19 2026

a(9) from Rhys Feltman, May 02 2026

Status

approved