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%I #66 Jan 27 2023 19:52:05
%S 1,1,1,2,5,16,55,224,978,4507,21430,104423,517897,2606185,13272978
%N Number of free polyominoes in {4,5} tessellation of the hyperbolic plane.
%H Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/a/200295/53884">Impress Donald Knuth by counting polyominoes on the hyperbolic plane</a>.
%H Don Hatch, <a href="http://www.plunk.org/~hatch/HyperbolicTesselations/">Hyperbolic Planar Tesselations: {4,5}</a>.
%H Peter Kagey, <a href="/A119611/a119611.pdf">Example of the a(5)=16 free pentominoes in {4,5} tessellation of the hyperbolic plane</a>.
%H Greg Malen, Érika Roldán, and Rosemberg Toalá-Enríquez, <a href="https://doi.org/10.1007/s00026-022-00631-1">Extremal {p, q}-Animals</a>, Ann. Comb. (2023), p. 3.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Polyomino.html">Polyomino</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Order-5_square_tiling">Order-5 square tiling</a>.
%e For n = 0,1,2,3 the polyominoes in the {4,5} tessellation of the hyperbolic plane are essentially same as the ordinary polyominoes in the plane (A000105), with redefinition of "straight line" and angular deficiency at a vertex.
%e For n = 4, the square tetromino does not exist. In its place is the cut-square, a pentagonal pentomino with one cell removed.
%e For n = 5, see links section.
%o Several working programs are available via the Code Golf Stack Exchange link.
%Y Cf. A000105.
%K nonn,more
%O 0,4
%A _Jonathan Vos Post_, Jun 04 2006
%E a(5) corrected by _Don Knuth_
%E a(6) corrected by _Christian Sievers_
%E a(7)-a(10) from _Christian Sievers_
%E a(11)-a(14) from _Ed Wynn_, Feb 14 2021
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