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A119611 Number of free polyominoes in {4,5} tessellation of the hyperbolic plane. 5
1, 1, 1, 2, 5, 16, 55, 224, 978, 4507, 21430 (list; graph; refs; listen; history; text; internal format)



Table of n, a(n) for n=0..10.

Code Golf Stack Exchange Impress Donald Knuth by counting polyominoes on the hyperbolic plane

Don Hatch, Hyperbolic Planar Tesselations: {4,5}.

Peter Kagey, Example of the a(5)=16 free pentominoes in {4,5} tessellation of the hyperbolic plane.

Eric Weisstein's World of Mathematics, Polyomino.

Wikipedia, Order-5 square tiling


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.

For n = 4, the square tetromino does not exist. In its place is the cut-square, a pentagonal pentomino with one cell removed.

For n = 5, see links section.


Cf. A000105.

Sequence in context: A333233 A019988 A137732 * A057973 A102461 A176332

Adjacent sequences:  A119608 A119609 A119610 * A119612 A119613 A119614




Jonathan Vos Post, Jun 04 2006


a(5) corrected by Don Knuth

a(6) corrected by Christian Sievers

a(7)-a(10) from Christian Sievers



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Last modified November 30 05:31 EST 2020. Contains 338781 sequences. (Running on oeis4.)