A352498 Number of complete triangulations of the Koch chain K_s.

1, 1, 2, 424, 975419632, 86131212354640695306944, 19668281895304112711343831241714273736245631706515584

Offset

0,3

Comments

The Koch chain K_s is a sequence of 2^s+1 points which form an x-monotone chain of unavoidable edges in the plane with the same combinatorial structure as the fractal Koch curve.

Given that the number of points already grows exponentially in s, the numbers of triangulations themselves have double exponential growth of roughly 9.083^(2^s), see Theorem 5 of Rutschmann, Wettstein (2022).

References

D. Rutschmann and M. Wettstein, "Chains, Koch Chains, and Point Sets with many Triangulations", 38th International Symposium on Computational Geometry (SOCG 2022), to appear.

Links

Table of n, a(n) for n=0..6.

D. Rutschmann and M. Wettstein, Chains, Koch Chains, and Point Sets with many Triangulations, arXiv preprint arXiv:2203.07584 [cs.CG], 2022.

Crossrefs

Product of A352496 and A352497.

Sequence in context: A373552 A332142 A109931 * A326364 A200951 A118710

Adjacent sequences: A352495 A352496 A352497 * A352499 A352500 A352501

Keyword

nonn

Author

Manuel Wettstein, Mar 18 2022

Status

approved