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A242823
Perimeter (rounded down) of Pi-shaped box fractal after n iterations.
1
1, 2, 5, 15, 39, 103, 269, 700, 1821, 4736, 12313, 32016, 83242, 216429, 562716, 1463063, 3803966, 9890311, 25714810, 66858508, 173832121, 451963515, 1175105140, 3055273364, 7943710747, 20653647942, 53699484649
OFFSET
0,2
COMMENTS
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.
LINKS
Eric Weisstein's World of Mathematics, Box Fractal
Wikipedia, Vicsek fractal
PROG
(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), ", "))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Kival Ngaokrajang, May 23 2014
STATUS
approved