A119611 Number of free polyominoes in {4,5} tessellation of the hyperbolic plane.

1, 1, 1, 2, 5, 16, 55, 224, 978, 4507, 21430, 104423, 517897, 2606185, 13272978

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.

Greg Malen, Érika Roldán, and Rosemberg Toalá-Enríquez, Extremal {p, q}-Animals, Ann. Comb. (2023), p. 3.

Eric Weisstein's World of Mathematics, Polyomino.

Wikipedia, Order-5 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 cut-square, 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