A197462 Number of free poly-[4.6.12]-tiles (holes allowed) with n cells (division into triangles is significant).

1, 3, 3, 9, 14, 38, 74, 185, 414, 1026, 2440, 6077, 14926, 37454, 93749, 237035, 599815, 1526020, 3889117, 9944523, 25475398, 65416733, 168277945, 433705325, 1119610147, 2894928713

Offset: 1

Author

Joseph Myers, Oct 15 2011

Keywords

• hard
• nonn

Comments

[4.6.12] refers to the face configuration of the kisrhombille tiling. - Peter Kagey, May 10 2021

References

• Branko Gruenbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, Sections 2.7, 6.2 and 9.4.

Links

• Peter Kagey, Illustration of a(4) = 9.
• Wikipedia, Kisrhombille tiling

Crossrefs

Cf. A197463, A197464.

Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197459 (rhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square).

Extensions

a(20)-a(26) from Aaron N. Siegel, Jun 03 2022