A293289 Number of level n squares on a Sierpinski carpet that intersect the edge of a circle with the same center and diameter.

1, 8, 28, 76, 204, 580, 1556, 4180, 11204, 29724, 79276, 212076, 565692, 1509332, 4026028, 10740796, 28646804, 76396620, 203728972, 543283204, 1448779164, 3863345612, 10302538780, 27473690092, 73263231116, 195369181668, 520985280228, 1389296277316, 3704793953044

Offset: 0

Author

Yi Yang, Oct 05 2017

Keywords

• nonn

Comments

There are 8^n level n squares on a Sierpinski carpet.

The terms of this sequence have a common factor 4 except a(0).

Lim_{n->infinity} a(n)/a(n-1) = 8/3.

Lim_{n->infinity} a(n)/(8/3)^n = 4.38167....

Links

• Yi Yang, Table of n, a(n) for n = 0..32
• Chyanog, Illustration of initial terms (the blue squares are counted)
• Wayne, Ickiverar, The C++ code generating the sequence

Crossrefs

Cf. A094976, A242118, A293288.