A293288 Number of level n squares on a Sierpinski carpet that are enclosed in a circle with the same center and diameter.

0, 0, 32, 332, 2908, 23900, 192844, 1547068, 12388068, 99135316, 793162780, 6345516140, 50764701756, 406119132924, 3248957101772, 25991667561644, 207933369171996, 1663467029827132, 13307736442512524, 106461892083564380, 851695138117736668, 6813561108806027412

Offset: 0

Author

Yi Yang, Oct 04 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.

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

Lim_{n->infinity} a(n)/8^n = 0.73872777586247800994....

Links

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

Crossrefs

Cf. A001018, A261849, A293289.