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A235648 Perimeter (rounded down) of a tetraflake-like fractal after n iterations, a(1) = 1 (see comments). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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).

LINKS

Table of n, a(n) for n=1..41.

Kival Ngaokrajang, Illustration of initial terms

Eric Weisstein's World of Mathematics, Box Fractal

Wikipedia, n-flake

Wikipedia, Vicsek Fractal

FORMULA

Floor((5*a(n-1)-2*(4*c(n-1)+3^(n-1)))/18) for n >1, a(1)=18, c(1)=1.

PROG

(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, ", ")); }

CROSSREFS

Cf. A241271, A235643.

Cf. A240523 (pentaflake), A240671 (heptaflake), A240572 (octaflake), A240733 (nonaflake), A240734 (decaflake), A240840 (hendecaflake), A240735 (dodecaflake), A240841 (tridecaflake).

Cf. A063628 (hexaflake).

Cf. A240916, A240917 (triflake-like); A238777 (tetraflake-like).

Sequence in context: A013982 A202411 A293161 * A051449 A018143 A281839

Adjacent sequences:  A235645 A235646 A235647 * A235649 A235650 A235651

KEYWORD

nonn

AUTHOR

Kival Ngaokrajang, Apr 20 2014

STATUS

approved

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Last modified February 25 22:44 EST 2020. Contains 332270 sequences. (Running on oeis4.)