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%I #13 Feb 15 2015 00:36:38
%S 1,2,5,15,39,103,269,700,1821,4736,12313,32016,83242,216429,562716,
%T 1463063,3803966,9890311,25714810,66858508,173832121,451963515,
%U 1175105140,3055273364,7943710747,20653647942,53699484649
%N Perimeter (rounded down) of Pi-shaped box fractal after n iterations.
%C 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 Kival Ngaokrajang, <a href="/A242823/a242823_1.pdf">Illustration of initial terms</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BoxFractal.html">Box Fractal</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Vicsek_fractal">Vicsek fractal</a>
%o (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 Cf. A001019, A005050, A154265.
%K nonn
%O 0,2
%A _Kival Ngaokrajang_, May 23 2014