A329927 a(n) is the number of squares with largest size after n iterations of the "Square Multiscale" substitution.

1, 1, 1, 1, 16, 1, 32, 1, 48, 1, 64, 256, 1, 80, 768, 1, 96, 1536, 1, 112, 2560, 4096, 1, 128, 3840, 16384, 1, 144, 5376, 40960, 1, 160, 7168, 81920, 65536, 1, 176, 9216, 143360, 327680, 1, 192, 11520, 229376, 983040, 1, 208, 14080, 344064, 2293760, 1048576, 1

Offset: 0

Author

Rémy Sigrist, Nov 24 2019

Keywords

• nonn

Comments

See A329919 for further details about the "Square Multiscale" substitution.

This sequence only contains ones and multiples of 16; the ones correspond to situations where the central square is the largest.

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, PARI program for A329927
• Yotam Smilansky, Yaar Solomon, Multiscale Substitution Tilings, arXiv:2003.11735 [math.DS], 2020.

Crossrefs

Cf. A328074, A329919.

Programs

PARI

See Links section.

Formula

a(n) = (A329919(n+1) - A329919(n)) / 16.