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
Examples
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.
Links
- 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.
Crossrefs
Cf. A000105.
Programs
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C
// See the Code Golf Stack Exchange link.
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GAP
# See the Code Golf Stack Exchange link.
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bc
/* See the Code Golf Stack Exchange link. */
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