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A354535
a(n) is the number of different tile sizes after n iterations of the "Square Multiscale" substitution.
3
1, 2, 3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20
OFFSET
0,2
COMMENTS
See A329919 for further details about the "Square Multiscale" substitution.
LINKS
Yotam Smilansky and Yaar Solomon, Multiscale Substitution Tilings, arXiv:2003.11735 [math.DS], 2020.
FORMULA
a(n+1) - a(n) = 0 or 1.
EXAMPLE
The first terms, alongside the corresponding sizes, are:
n a(n) Tile sizes
- ---- -----------------------------------------------
0 1 {1}
1 2 {3/5, 1/5}
2 3 {9/25, 1/5, 3/25}
3 4 {27/125, 1/5, 3/25, 9/125}
4 5 {1/5, 81/625, 3/25, 9/125, 27/625}
5 5 {81/625, 3/25, 9/125, 27/625, 1/25}
6 6 {3/25, 243/3125, 9/125, 27/625, 1/25, 81/3125}
7 6 {243/3125, 9/125, 27/625, 1/25, 81/3125, 3/125}
PROG
(PARI) { sc = [1]; for (n=0, 68, print1 (#sc", "); s = vecmax(sc); sc = setunion(setminus(sc, [s]), Set([3*s/5, s/5]))) }
CROSSREFS
Sequence in context: A372306 A327705 A104135 * A276656 A373119 A309250
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Aug 17 2022
STATUS
approved