A390200 a(n) is the number of n-celled polyplets (polyominoes connected at edges or corners) in the {4,5} tessellation of the hyperbolic plane.

1, 2, 10, 72, 710, 8026, 98353, 1261889

Offset

1,2

Comments

This sequence was calculated in the context of a project in collaboration with Érika Roldán, and Rosemberg Toalá-Enríquez.

The term a(8) was computed by direct canonical expansion using exact algebraic matrices over Q(sqrt(2), sqrt(5)), with cells represented as cosets of the face stabilizer in the Coxeter group [4,5]. - Pragyaan Gaur, Jun 03 2026

Links

Table of n, a(n) for n=1..8.

Pragyaan Gaur, Hyperbolic Polyplet Enumerator (contains Python implementations for exact enumeration).

Prog

(Python) # See GitHub link for exact algebraic matrix implementation.

Crossrefs

Cf. A119611, A030222.

Sequence in context: A204808 A084844 A144011 * A238085 A277502 A231039

Adjacent sequences: A390197 A390198 A390199 * A390201 A390202 A390203

Keyword

nonn,more

Author

John Mason, Nov 02 2025

Extensions

a(8) from Pragyaan Gaur, Jun 03 2026

Status

approved