

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, 104423, 517897, 2606185, 13272978
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OFFSET

0,4


LINKS

Table of n, a(n) for n=0..14.
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, Order5 square tiling


EXAMPLE

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 cutsquare, a pentagonal pentomino with one cell removed.
For n = 5, see links section.


PROG

Several working programs are available via the Code Golf Stack Exchange link.


CROSSREFS

Cf. A000105.
Sequence in context: A333233 A019988 A137732 * A057973 A102461 A176332
Adjacent sequences: A119608 A119609 A119610 * A119612 A119613 A119614


KEYWORD

nonn,more


AUTHOR

Jonathan Vos Post, Jun 04 2006


EXTENSIONS

a(5) corrected by Don Knuth
a(6) corrected by Christian Sievers
a(7)a(10) from Christian Sievers
a(11)a(14) from Ed Wynn, Feb 14 2021


STATUS

approved



