A367174 a(n) = the maximum number of distinct tilings of a polyhex of size n using any combination of polyhex tiles of sizes 1 through n.

1, 2, 5, 13, 34, 89, 316, 830, 2179, 7781

Offset

1,2

Comments

The sequence considers reflections and rotations as distinct tilings. The polyhexes being tiled and the tiles themselves may be with or without holes.

A001519(n) is the number of tilings for a "zigzag" polyhex with n cells:

o---o- --o

/ \ / \ ... /

o---o--- o - Charlie Neder, Sep 10 2025

a(n) is the maximum composition number of the adjacency graph of a polyhex of size n. - Pontus von Brömssen, Sep 16 2025

Links

Table of n, a(n) for n=1..10.

Example

a(3) = 5 because the polyhex of size 3 that has each cell touching both the other cells can be tiled by (1) a polyhex of size 3, (2) 3 polyhexes of size 1, and (3) a polyhex of size 1 and a polyhex of size 2 in three distinct ways.

Crossrefs

Cf. A000228, A001519, A367172, A367173.

Sequence in context: A122367 A367658 A114299 * A112842 A097417 A367657

Adjacent sequences: A367171 A367172 A367173 * A367175 A367176 A367177

Keyword

nonn,more

Author

John Mason from an idea of Craig Knecht, Nov 07 2023

Extensions

a(5) corrected by Charlie Neder, Sep 10 2025

a(7), a(8), and a(10) corrected by Pontus von Brömssen, Sep 16 2025

Status

approved