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Number of polyominoes with n cells that tile the plane by translation.
10

%I #16 Jun 26 2021 03:57:29

%S 1,1,2,5,9,24,41,121,213,522,783,2712,3179,8672,16621,37415,48558,

%T 154660,185007,573296,876633,1759730,2606543,8768743,10774339

%N Number of polyominoes with n cells that tile the plane by translation.

%D Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987, Section 9.4.

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

%e For n = 5, all 12 of the free pentominoes tile the plane by translation except for the R, T, and U pentominoes, so a(5) = 12 - 3 = 9.

%Y Cf. A054359, A075199, A075200, A075201, A075202, A075203, A075204, A075205, A075206, A075207, A075216.

%K hard,nonn

%O 1,3

%A _Joseph Myers_, Sep 08 2002

%E More terms from _Joseph Myers_, Nov 04 2003

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