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Number of free poly-[4.6.12]-tiles (holes allowed) with n cells (division into triangles is significant).
14

%I #18 Jun 03 2022 11:17:01

%S 1,3,3,9,14,38,74,185,414,1026,2440,6077,14926,37454,93749,237035,

%T 599815,1526020,3889117,9944523,25475398,65416733,168277945,433705325,

%U 1119610147,2894928713

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

%C [4.6.12] refers to the face configuration of the kisrhombille tiling. - _Peter Kagey_, May 10 2021

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

%H Peter Kagey, <a href="/A197462/a197462.pdf">Illustration of a(4) = 9</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Truncated_trihexagonal_tiling#Kisrhombille_tiling">Kisrhombille tiling</a>

%Y Cf. A197463, A197464.

%Y 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).

%K hard,nonn

%O 1,2

%A _Joseph Myers_, Oct 15 2011

%E a(20)-a(26) from _Aaron N. Siegel_, Jun 03 2022