A393325 Triangle T(n,s) read by rows: The number of ways of inserting smaller hexagons of edge lengths s into a larger amount hexagon of edge length n.

2, 19, 2, 1425, 8, 2, 799779, 46, 8, 2, 3322809333, 865, 20, 8, 2

Offset

1,1

Comments

The smaller hexagons are placed in the larger hexagon on a commensurate triangular mesh. The smaller hexagons must not overlap and must not stretch beyond the perimeter of the larger hexagon. The configurations are considered fixed, i.e., rotations and flips of the set of the smaller hexagons may create different configurations. The filling factor may be smaller than 1: the smaller hexagons do not need to cover the larger hexagon entirely but may leave patches of unit triangles.

Links

Table of n, a(n) for n=1..15.

R. J. Mathar, Tiling hexagons with smaller hexagons and unit triangles (2016) vixra:1608.0380.

Formula

T(n,n)=2 counts one way of not placing a smaller hexagon plus one way of placing a hexagon of the same size

Example

The triangle starts in row n>=1 with columns 1<=s<=n as
2;
19, 2;
1425, 8, 2 ;
799779, 46, 8, 2 ;
3322809333, 865, 20, 8, 2 ;
?,          27566, 85, 20, 8, 2 ;
? ,         2186070, 984, 38, 20, 8, 2 ;

Crossrefs

Sequence in context: A221229 A221602 A354207 * A358980 A092120 A059706

Adjacent sequences: A393322 A393323 A393324 * A393326 A393327 A393328

Keyword

nonn,tabl

Author

R. J. Mathar, Feb 11 2026

Status

approved