OFFSET
0,6
COMMENTS
We apply the following substitutions to transform A(m) into A(m+1):
t----t+u---t+u----u
| | | |
| | | |
t-----u t+v--t+u+v-t+u+w--u+w
| | ___\ | | | |
| | / | | | |
v-----w t+v--t+v+w-u+v+w--u+w
| | | |
| | | |
v----v+w---v+w----w
A(m) has 3^m+1 rows.
As m gets larger, A(m) exhibits interesting fractal features (see illustrations in Links section).
LINKS
Rémy Sigrist, Representation of the multiples of 2 in T(6)
Rémy Sigrist, Representation of the multiples of 3 in T(6)
Rémy Sigrist, Representation of the multiples of 5 in T(6)
Rémy Sigrist, PARI program
Rémy Sigrist, Nonperiodic tilings related to Stern's diatomic series and based on tiles decorated with elements of Fp, arXiv:2301.06039 [math.CO], 2023.
EXAMPLE
Square A(0) is:
1 1
1 1
Square A(1) is:
1 2 2 1
2 3 3 2
2 3 3 2
1 2 2 1
Square A(2) is:
1 3 3 2 4 4 2 3 3 1
3 5 6 5 7 7 5 6 5 3
3 6 7 5 8 8 5 7 6 3
2 5 5 3 6 6 3 5 5 2
4 7 8 6 9 9 6 8 7 4
4 7 8 6 9 9 6 8 7 4
2 5 5 3 6 6 3 5 5 2
3 6 7 5 8 8 5 7 6 3
3 5 6 5 7 7 5 6 5 3
1 3 3 2 4 4 2 3 3 1
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Rémy Sigrist, Jul 30 2022
STATUS
approved