cp's OEIS Frontend

A354535 a(n) is the number of different tile sizes after n iterations of the "Square Multiscale" substitution.

%I A354535 #16 Aug 21 2022 06:12:34
%S A354535 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,
%T A354535 13,13,13,14,14,14,14,14,15,15,15,15,15,16,16,16,16,16,17,17,17,17,17,
%U A354535 17,18,18,18,18,18,18,19,19,19,19,19,19,20,20,20,20,20
%N A354535 a(n) is the number of different tile sizes after n iterations of the "Square Multiscale" substitution.
%C A354535 See A329919 for further details about the "Square Multiscale" substitution.
%H A354535 Rémy Sigrist, <a href="/A354535/b354535.txt">Table of n, a(n) for n = 0..10000</a>
%H A354535 Yotam Smilansky and Yaar Solomon, <a href="https://arxiv.org/abs/2003.11735">Multiscale Substitution Tilings</a>, arXiv:2003.11735 [math.DS], 2020.
%F A354535 a(n+1) - a(n) = 0 or 1.
%e A354535 The first terms, alongside the corresponding sizes, are:
%e A354535   n  a(n)  Tile sizes
%e A354535   -  ----  -----------------------------------------------
%e A354535   0     1  {1}
%e A354535   1     2  {3/5, 1/5}
%e A354535   2     3  {9/25, 1/5, 3/25}
%e A354535   3     4  {27/125, 1/5, 3/25, 9/125}
%e A354535   4     5  {1/5, 81/625, 3/25, 9/125, 27/625}
%e A354535   5     5  {81/625, 3/25, 9/125, 27/625, 1/25}
%e A354535   6     6  {3/25, 243/3125, 9/125, 27/625, 1/25, 81/3125}
%e A354535   7     6  {243/3125, 9/125, 27/625, 1/25, 81/3125, 3/125}
%o A354535 (PARI) { sc = [1]; for (n=0, 68, print1 (#sc", "); s = vecmax(sc); sc = setunion(setminus(sc,[s]), Set([3*s/5, s/5]))) }
%Y A354535 Cf. A329919, A329927.
%K A354535 nonn
%O A354535 0,2
%A A354535 _Rémy Sigrist_, Aug 17 2022