A293289 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

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