A293288 -id:A293288 - cp's OEIS frontend

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

Yi Yang, Oct 05 2017

nonn

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....

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

Cf. A094976, A242118, A293288.

A329302 Number of level-n cubes on a Menger Sponge that are enclosed in the inscribed sphere of the starting cube.

Original entry on oeis.org

0, 44, 2320, 54800, 1146112, 23278472, 468028264, 9376805048, 187644496672, 3753613318520, 75077089399408, 1501573939443704, 30031693123408792, 600635291349699440, 12012715352891236816, 240254370564131706488, 4805087834658423387496, 96101759515675744360544

Offset: 1

Zhao Hui Du, Nov 30 2019

nonn

A level-n cube is understood to be enclosed in a sphere if each of its 8 vertices lies either inside or on the surface of the sphere.

This sequence is a 3D extension to A293288.

Sierpinski copper coin, Table of results computed by Hong Yang Cao (in Chinese).
Wikipedia, Menger sponge.

Cf. A117609, A120884, A293288.

a(9)-a(18) from Ickiverar added by Zhao Hui Du, Jan 10 2020

cp's OEIS Frontend

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

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