A197156 Number of free poly-[3^3.4^2]-tiles (polyhouses) (holes allowed) with n cells.

1, 3, 5, 20, 56, 225, 819, 3333, 13336, 55231, 229146, 963284, 4068503, 17301000, 73893082, 317013121, 1364917667, 5896350458, 25545737979, 110968732581

Offset: 1

Author

Joseph Myers, Oct 10 2011

Keywords

• hard
• more
• 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) = 5.
• Brendan Owen, Polyhouses (gives a(1)-a(10)).
• Wikipedia, Prismatic pentagonal tiling

Crossrefs

Cf. A197157, A197158.

Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197159 (floret 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