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Number of generalized polyforms on the truncated square tiling with n cells.
14

%I #34 Jan 15 2023 09:37:14

%S 1,2,2,7,22,93,413,2073,10741,57540,312805,1722483,9564565,53489304,

%T 300840332,1700347858,9650975401

%N Number of generalized polyforms on the truncated square tiling with n cells.

%C This sequence counts "free" polyforms where holes are allowed. This means that two polyforms are considered the same if one is a rigid transformation (translation, rotation, reflection or glide reflection) of the other.

%C a(n) >= A343417(n), the number of (n-k)-polyominoes with k distinguished vertices.

%H Peter Kagey, <a href="/A343577/a343577.hs.txt">Haskell program for computing sequence</a>.

%H Peter Kagey, <a href="/A343577/a343577.pdf">The a(3) = 7 generalized polyforms on the truncated square tiling with 3 cells</a>.

%H John Mason, <a href="/A343577/a343577_1.pdf">Illustration of equivalence between truncated square polyforms and a mixture of crosses and squares</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Truncated_square_tiling">Truncated Square Tiling</a>

%Y Analogous for other tilings: A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197459 (rhombille), A197462 (kisrhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal).

%K nonn,more

%O 0,2

%A _Peter Kagey_, Apr 20 2021

%E a(11) from _Drake Thomas_, May 02 2021

%E a(12)-a(16) from _John Mason_, Mar 20 2022