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A235648
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Perimeter (rounded down) of a tetraflake-like fractal after n iterations, a(1) = 1 (see comments).
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2
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1, 1, 2, 3, 4, 7, 10, 16, 25, 39, 61, 97, 155, 249, 404, 657, 1073, 1759, 2892, 4768, 7877, 13036, 21602, 35838, 59508, 98885, 164416, 273502, 455137, 757628, 1261470, 2100791, 3499106, 5828894, 9710891, 16179575, 26958966, 44922289, 74858052, 124746848, 207889317
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OFFSET
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1,3
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COMMENTS
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Construction rule is same as for box and Vicsek fractals, but uses 6 boxes at initial stage (n = 1) and has only one symmetrical axis. The scale factor of these fractals is 1/3. The actual tetraflake fractals have a scale factor of 1/2.
The total number of sides at different lengths of a tetraflake-like fractal after n iterations is A235643(n). The total number of holes is A241271(n+1).
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LINKS
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FORMULA
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Floor((5*a(n-1)-2*(4*c(n-1)+3^(n-1)))/18) for n >1, a(1)=18, c(1)=1.
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PROG
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(PARI){a=18; c=1; print1(1, ", "); for (n=1, 50, c=4*c+3^(n-1); a=5*a-2*c; aa=floor((a*(1/3)^n)/18); print1(aa, ", ")); }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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