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Number of polyominoes with n cells without holes that do not tile the plane.
4

%I #17 Dec 04 2023 06:40:12

%S 0,0,0,0,0,0,3,20,198,1390,9474,35488,178448,696371,2721544,10683110,

%T 41334494,155723774,596182769,2257379379,8587521496,32688629235,

%U 124568505590,475147925759,1815832051949

%N Number of polyominoes with n cells without holes that do not tile the plane.

%D Posting by Glenn C. Rhoads (rhoads(AT)paul.rutgers.edu) to rec.puzzles, Feb 17 2000.

%H Craig S. Kaplan, <a href="https://isohedral.ca/heesch-numbers-of-unmarked-polyforms/">Heesch Numbers of Unmarked Polyforms</a>

%H Craig S. Kaplan, <a href="https://arxiv.org/abs/2105.09438">Heesch Numbers of Unmarked Polyforms</a>, arXiv:2105.09438 [cs.CG], 2021. See Table 1 and Table 2.

%H Joseph Myers, <a href="http://www.polyomino.org.uk/mathematics/polyform-tiling/">Polyomino tiling</a>

%e a(7) = 3.

%Y Cf. A000104, A054360, A070768, A071334.

%K nonn,hard,more

%O 1,7

%A Joe Keane (jgk(AT)jgk.org)

%E Corrected and extended by _Joseph Myers_, May 05 2002

%E More terms from _Joseph Myers_, Nov 04 2003

%E a(24) and a(25) from _Joseph Myers_, Nov 17 2010