This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A242823 #14 Feb 16 2025 08:33:22
%S A242823 1,2,5,15,39,103,269,700,1821,4736,12313,32016,83242,216429,562716,
%T A242823 1463063,3803966,9890311,25714810,66858508,173832121,451963515,
%U A242823 1175105140,3055273364,7943710747,20653647942,53699484649
%N A242823 Perimeter (rounded down) of Pi-shaped box fractal after n iterations.
%C A242823 Let 13 boxes be placed into a 5 X 5 square grid, arranged in the shape of a capital letter Pi (see illustration). Also let the initial side length of a box = 1/28. The side length of a box after n iterations will be 1/(4*A005050(n)) i.e., 1/28, 1/140, 1/700, 1/3500, ... The sides count (any lengths) is 12*A001019(n), i.e., 12, 108, 972, 8748, ... The Hausdorff dimension = log(13)/log(5) = 1.593692641167... or A154265.
%H A242823 Kival Ngaokrajang, <a href="/A242823/a242823_1.pdf">Illustration of initial terms</a>
%H A242823 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BoxFractal.html">Box Fractal</a>
%H A242823 Wikipedia, <a href="http://en.wikipedia.org/wiki/Vicsek_fractal">Vicsek fractal</a>
%o A242823 (PARI){a=28;b=1;print1(1,", "); for (n=2,50, b=b*0.2; a=(a*13-16*2^(n-1)-8); print1(floor(a*b/28),", "))}
%Y A242823 Cf. A001019, A005050, A154265.
%K A242823 nonn
%O A242823 0,2
%A A242823 _Kival Ngaokrajang_, May 23 2014