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A343577 Number of generalized polyforms on the truncated square tiling with n cells.

%I A343577 #40 May 26 2025 11:49:26
%S A343577 1,2,2,7,22,93,413,2073,10741,57540,312805,1722483,9564565,53489304,
%T A343577 300840332,1700347858,9650975401
%N A343577 Number of generalized polyforms on the truncated square tiling with n cells.
%C A343577 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 A343577 a(n) >= A343417(n), the number of (n-k)-polyominoes with k distinguished vertices.
%H A343577 Kadon Enterprises, <a href="https://gamepuzzles.com/ochom.htm">Interesting solutions: Ochominoes</a>.
%H A343577 Peter Kagey, <a href="/A343577/a343577.hs.txt">Haskell program for computing sequence</a>.
%H A343577 Peter Kagey, <a href="/A343577/a343577.pdf">The a(3) = 7 generalized polyforms on the truncated square tiling with 3 cells</a>.
%H A343577 Peter Kagey, <a href="/A343577/a343577_2.pdf">The a(5) = 93 generalized polyforms on the truncated square tiling with 5 cells</a>.
%H A343577 John Mason, <a href="/A343577/a343577_1.pdf">Illustration of equivalence between truncated square polyforms and a mixture of crosses and squares</a>.
%H A343577 Wikipedia, <a href="https://en.wikipedia.org/wiki/Truncated_square_tiling">Truncated Square Tiling</a>
%Y A343577 Cf. A121197 (one-sided).
%Y A343577 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 A343577 nonn,more
%O A343577 0,2
%A A343577 _Peter Kagey_, Apr 20 2021
%E A343577 a(11) from _Drake Thomas_, May 02 2021
%E A343577 a(12)-a(16) from _John Mason_, Mar 20 2022