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

0,2

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

Crossrefs

Cf. A094976, A242118, A293288.

Sequence in context: A209408 A316214 A134638 * A305638 A331757 A130129

Adjacent sequences: A293286 A293287 A293288 * A293290 A293291 A293292

Keyword

nonn

Author

Yi Yang, Oct 05 2017

Status

approved