A235648 Perimeter (rounded down) of a tetraflake-like fractal after n iterations, a(1) = 1 (see comments).

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

Offset: 1

Author

Kival Ngaokrajang, Apr 20 2014

Keywords

• nonn

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

• Kival Ngaokrajang, Illustration of initial terms
• Eric Weisstein's World of Mathematics, Box Fractal
• Wikipedia, n-flake
• Wikipedia, Vicsek Fractal

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).

Programs

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,", "));}

Formula

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