A197159 Number of free poly-[3^4.6]-tiles (holes allowed) with n cells.

1, 3, 8, 25, 80, 291, 1036, 3875, 14561, 55624, 213951, 830712, 3244355, 12747718, 50320659, 199491045, 793754027, 3168756843, 12687184463, 50932363171

Offset: 1

Author

Joseph Myers, Oct 10 2011

Keywords

• hard
• nonn

References

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

Links

• Peter Kagey, Example illustrating that a(3) = 8.
• Wikipedia, Floret pentagonal tiling

Crossrefs

Cf. A197160.

Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197459 (rhombille), A197462 (kisrhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square).

Extensions

a(16)-a(20) from Bert Dobbelaere, Jun 02 2025